Behavior of Solutions of Quasilinear Elliptic Inequalities

A. A. Kon'kov

Contemporary Mathematics. Fundamental Directions, Partial differential equations, Tome 7 (2004), pp. 3-158.

Bibliographie

[1] Bagirov L. A., Kondratev V. A., “Ob ellipticheskikh uravneniyakh v $\mathbb R^n$”, Differents. uravneniya, 11:3 (1975), 498–504 | MR | Zbl

[2] Bers L., Dzhon F., Shekhter M., Uravneniya s chastnymi proizvodnymi, Mir, M., 1966 | MR | Zbl

[3] Blokhina G. N., “Teoremy tipa Fragmena–Lindelëfa dlya lineinogo ellipticheskogo uravneniya 2-go poryadka”, Dokl. AN SSSR, 4 (1965), 727–730

[4] Blokhina G. N., “Teoremy tipa Fragmena–Lindelëfa dlya lineinogo ellipticheskogo uravneniya vtorogo poryadka”, Mat. sb., 82(124):4(8) (1970), 507–531 | MR | Zbl

[5] Gerver M. L., Landis E. M., “Odno obobschenie teoremy o srednem dlya mnogikh peremennykh”, Dokl. AN SSSR, 4 (1962), 761–764 | MR

[6] Kiguradze I. T., “O monotonnykh resheniyakh nelineinykh obyknovennykh differentsialnykh uravnenii”, Dokl. AN SSSR, 181:5 (1968), 1054–1057 | MR | Zbl

[7] Kiguradze I. T., Chanturiya T. A., Asimptoticheskie svoistva reshenii neavtonomnykh obyknovennykh differentsialnykh uravnenii, Nauka, M., 1990 | Zbl

[8] Kondratev V. A., “O kachestvennykh svoistvakh reshenii polulineinykh ellipticheskikh uravnenii”, Trudy seminara im. I. G. Petrovskogo, 1992, no. 16, 186–190

[9] Kondratev V. A., Konkov A. A., “O svoistvakh reshenii odnogo klassa nelineinykh uravnenii vtorogo poryadka”, Mat. sb., 185:9 (1994), 81–94 | MR

[10] Kondratev V. A., Landis E. M., “Polulineinye uravneniya”, Uspekhi mat. nauk, 42:5 (1987), 233–234

[11] Kondratev V. A., Landis E. M., “O kachestvennykh svoistvakh reshenii odnogo nelineinogo uravneniya vtorogo poryadka”, Mat. sb., 135:3 (1988), 346–360 | MR | Zbl

[12] Kondratev V. A., Landis E. M., “Kachestvennaya teoriya lineinykh differentsialnykh uravnenii v chastnykh proizvodnykh vtorogo poryadka”, Itogi nauki i tekhniki. Sovremennye problemy matematiki. Fundamentalnye napravleniya, 32, VINITI, M., 1988, 99–215 | MR

[13] Kondratev V. A., Landis E. M., “Polulineinye uravneniya vtorogo poryadka s neotritsatelnoi kharakteristicheskoi formoi”, Mat. zametki, 44:4 (1988), 457–468 | MR | Zbl

[14] Kondratev V. A., Oleinik O. A., “O povedenii na beskonechnosti odnogo klassa nelineinykh ellipticheskikh uravnenii v tsilindricheskoi oblasti”, Dokl. RAN, 341:4 (1995), 446–449 | MR | Zbl

[15] Kondratev V. A., Eidelman S. D., “O polozhitelnykh resheniyakh nekotorykh kvazilineinykh uravnenii”, Dokl. RAN, 331:3 (1993), 278–280 | MR | Zbl

[16] Kondratev V. A., Eidelman S. D., “O polozhitelnykh resheniyakh kvazilineinykh ellipticheskikh uravnenii vtorogo poryadka”, Dokl. RAN, 334:4 (1994), 427–428 | MR | Zbl

[17] Konkov A. A., “O povedenii na beskonechnosti reshenii odnogo klassa nelineinykh uravnenii vtorogo poryadka”, Mat. zametki, 60:1 (1996), 30–39 | MR | Zbl

[18] Konkov A. A., “O povedenii reshenii kvazilineinykh ellipticheskikh neravenstv, soderzhaschikh chleny s mladshimi proizvodnymi”, Mat. zametki, 64:6 (1998), 946–949 | MR | Zbl

[19] Konkov A. A., “O neotritsatelnykh resheniyakh kvazilineinykh ellipticheskikh neravenstv”, Izv. RAN. Ser. Mat., 63:2 (1999), 41–126 | MR | Zbl

[20] Konkov A. A., “O povedenii reshenii kvazilineinykh ellipticheskikh neravenstv v okrestnosti osoboi tochki”, Dokl. RAN, 366:5 (1999), 595–598 | MR | Zbl

[21] Konkov A. A., “O neotritsatelnykh resheniyakh kvazilineinykh ellipticheskikh neravenstv v oblastyakh, raspolozhennykh v sloe”, Differents. uravneniya, 36:7 (2000), 889–897 | MR | Zbl

[22] Konkov A. A., “O resheniyakh kvazilineinykh ellipticheskikh neravenstv, obraschayuschikhsya v nul v okrestnosti beskonechnosti”, Mat. zametki, 67:1 (2000), 153–156 | MR | Zbl

[23] Konkov A. A., “O resheniyakh neavtonomnykh obyknovennykh differentsialnykh uravnenii”, Izv. RAN. Ser. Mat., 65:2 (2001), 81–126 | MR | Zbl

[24] Konkov A. A., “O svoistvakh reshenii ellipticheskikh neravenstv s nelineinostyu v glavnoi chasti”, Dokl. RAN, 383:1 (2002), 15–19 | MR

[25] Konkov A. A., “Teoremy sravneniya dlya ellipticheskikh neravenstv s nelineinostyu v glavnoi chasti”, Uspekhi mat. nauk, 57:3 (2002), 141–142 | MR

[26] Konkov A. A., “Povedenie reshenii ellipticheskikh neravenstv v oblastyakh proizvolnoi geometrii”, Dokl. RAN, 387:5 (2002), 604–607 | MR

[27] Kurta V. V., Nekotorye voprosy kachestvennoi teorii nelineinykh differentsialnykh uravnenii vtorogo poryadka, Dis. doktora fiz.-mat. nauk, MIAN, M., 1994

[28] Kurta V. V., “K voprosu ob otsutstvii tselykh polozhitelnykh reshenii u polulineinykh ellipticheskikh uravnenii”, Matem. zametki, 65:4 (1999), 552–561 | MR | Zbl

[29] Kurta V. V., “K voprosu ob otsutstvii polozhitelnykh reshenii u ellipticheskikh uravnenii”, Mat. zametki, 65:4 (1999), 552–561 | MR | Zbl

[30] Kurta V. V., “Ob otsutstvii polozhitelnykh reshenii u polulineinykh ellipticheskikh uravnenii”, Tr. MIAN, 227, 1999, 162–169 | MR | Zbl

[31] Ladyzhenskaya O. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Nauka, M., 1964 | MR

[32] Landis E. M., “Nekotorye voprosy kachestvennoi teorii ellipticheskikh uravnenii vtorogo poryadka”, Uspekhi mat. nauk, 18:4 (1963), 3–62 | MR

[33] Landis E. M., Uravneniya vtorogo poryadka ellipticheskogo i parabolicheskogo tipov, Nauka, M., 1971 | MR

[34] Landis E. M., “O povedenii reshenii ellipticheskikh uravnenii vysokogo poryadka v neogranichennykh oblastyakh”, Tr. Mosk. mat. ob-va, 31 (1974), 35–58 | MR | Zbl

[35] Landkof N. S., Osnovy sovremennoi teorii potentsiala, Nauka, M., 1966 | MR | Zbl

[36] Laptev G. G., “Otsutstvie globalnykh polozhitelnykh reshenii sistem polulineinykh ellipticheskikh neravenstv v konusakh”, Izv. RAN. Ser. Mat., 64:6 (2000), 107–124 | MR | Zbl

[37] Laptev G. G., “Ob otsutstvii reshenii odnogo klassa singulyarnykh polulineinykh differentsialnykh neravenstv”, Tr. MIAN, 232, 2001, 223–235 | MR | Zbl

[38] Mazya V. G., “O nepreryvnosti v granichnoi tochke reshenii kvazilineinykh ellipticheskikh uravnenii”, Vestn. LGU, 1972, no. 13, 42–55

[39] Mazya V. G., Prostranstva S. L. Soboleva, Izd-vo LGU, L., 1985 | MR

[40] Mitidieri E., Pokhozhaev S. I., “Otsutstvie globalnykh polozhitelnykh reshenii dlya kvazilineinykh ellipticheskikh neravenstv”, Dokl. RAN, 359:4 (1998), 456–460 | MR | Zbl

[41] Mitidieri E., Pokhozhaev S. I., “Otsutstvie polozhitelnykh reshenii dlya kvazilineinykh ellipticheskikh zadach v $\mathbb R^n$”, Tr. MIAN, 227, 1999, 192–222 | MR | Zbl

[42] Mitidieri E., Pokhozhaev S. I., “Otsutstvie polozhitelnykh reshenii dlya sistem kvazilineinykh ellipticheskikh uravnenii i neravenstv v $\mathbb R^n$”, Dokl. RAN, 366:1 (1999), 13–17 | MR

[43] Mitidieri E., Pokhozhaev S. I., Apriornye otsenki i otsutstvie reshenii nelineinykh uravnenii i neravenstv v chastnykh proizvodnykh, Nauka, M., 2001 | MR

[44] Pontryagin L. S., Obyknovennye differentsialnye uravneniya, Nauka, M., 1974 | MR

[45] Pokhozhaev S. I., “O kraevoi zadache dlya uravneniya $\Delta u=u^2$”, Dokl. AN SSSR, 140:3 (1961), 518–521

[46] Pokhozhaev S. I., “O razreshimosti ellipticheskikh uravnenii v $\mathbb R^n$ s superkriticheskim pokazatelem nelineinosti”, Dokl. AN SSSR, 313:6 (1990), 1356–1360 | MR | Zbl

[47] Pokhozhaev S. I., “O tselykh resheniyakh odnogo klassa kvazilineinykh ellipticheskikh uravnenii”, Dokl. AN SSSR, 318:6 (1991), 1319–1324 | MR | Zbl

[48] Pokhozhaev S. I., “Ob asimptotike tselykh radialnykh reshenii kvazilineinykh ellipticheskikh uravnenii”, Dokl. AN SSSR, 320:4 (1991), 808–813 | MR | Zbl

[49] Pokhozhaev S. I., “O tselykh resheniyakh kvazilineinykh ellipticheskikh uravnenii”, Dokl. AN SSSR, 318:4 (1991), 815–820 | MR | Zbl

[50] Pokhozhaev S. I., “O tselykh radialnykh resheniyakh kvazilineinykh ellipticheskikh uravnenii”, Tr. MIAN, 204, 1993, 251–273 | MR | Zbl

[51] Pokhozhaev S. I., “Suschestvenno nelineinye emkosti, indutsirovannye differentsialnymi operatorami”, Dokl. RAN, 357:5 (1997), 592–594 | MR | Zbl

[52] Khalmosh P., Teoriya mery, IL, M., 1953

[53] Amann H., Fila M., “A Fujita-type theorem for the Laplace equation with a dynamical boundary condition”, Acta Math. Univ. Comenian, 66 (1997), 321–328 | MR | Zbl

[54] Arend W., Batty C., Benilan Ph., “Asymptotic stability of Schrödinger semigroups”, Math. Z., 209:4 (1992), 511–518 | DOI | MR | Zbl

[55] Bangle C., Essen M., “On positive solutions of Emden equations in cone-like domains”, Arch. Ration. Mech. Anal., 112 (1990), 319–338 | DOI | MR

[56] Baras P., Pierre M., “Singularites eliminables pour des equations semilineaires”, Ann. Inst. Fourier, 34 (1984), 182–206 | MR

[57] Baras P., Pierre M., “Critere d'existence de solutions positives pour des equations semilineaires non monotones”, Ann. Inst. H. Poincaré, 2 (1985), 185–212 | MR | Zbl

[58] Bebernes J., “Blowup — when, where, and how?”, Bull. Soc. Math. Belg. A, 40 (1988), 3–45 | MR | Zbl

[59] Benguria R., Lorca S., Yarur C., “Nonexistence of positive solutions of semilinear elliptic equations”, Duke Math. J., 74 (1994), 615–634 | DOI | MR | Zbl

[60] Berestycki H., Nirenberg L., “Some qualitative properties of solutions of semilinear elliptic equations in cylindrical domains”, Analysis (volume dedicated to J. Moser), Academic Press, New York, 1990, 115–164 | MR

[61] Berestycki H., Capuzzo Dolcetta I., Nirenberg L., “Problèmes elliptiques indéfinis et théorèmes de Liouville non linéaires”, C. R. Acad. Sci. Paris. Ser. 1, 317 (1993), 945–950 | MR | Zbl

[62] Berestycki H., Capuzzo Dolcetta I., Nirenberg L., “Superlinear indefinite elliptic problems and nonlinear Liouville theorem”, Top. Meth. Nonlin. Anal., 4 (1995), 59–78 | MR

[63] Bidaut-Veron M.-F., “Local and global behavior of solutions of quasilinear equations of Emden–Fowler type”, Arch. Ration. Mech. Anal., 107 (1989), 293–324 | DOI | MR | Zbl

[64] Bidaut-Veron M.-F., Grillot P., “Asymptotic behavior of elliptic system with mixed absoption and source terms”, Asymp. Anal., 19 (1999.), 117–147 | MR | Zbl

[65] Bidaut-Veron M.-F., Raoux T., “Asymptotics of solutions of some nonlinear elliptic systems”, Commun. Part. Diff. Eq., 21 (1996), 1035–1086 | DOI | MR | Zbl

[66] Bidaut-Veron M.-F., Veron L., “Nonlinear elliptic equations on compact Riemannian manifolds and asymptotics of Emden equations”, Invent. Math., 106 (1991), 489–539 | DOI | MR | Zbl

[67] Birindelli I., Mitidieri E., “Liouville theorems for elliptic inequalities and applications”, Proc. Roy. Soc. Edinburgh A, 128 (1998), 1217–1247 | MR | Zbl

[68] Brezis H., Strauss W. A., “Semilinear second-order elliptic equations in $L^1$”, J. Math. Soc. Japan, 25 (1973), 565–590 | DOI | MR | Zbl

[69] Brezis H., Veron L., “Removable singularities of some nonlinear elliptic equations”, Arch. Ration. Mech. Anal., 75 (1980), 1–6 | DOI | MR | Zbl

[70] Brezis H., Cabre X., “Some simple nonlinear PDEs without solutions”, Boll. Unione Mat. Ital. B, 8 (1998), 223–262 | MR | Zbl

[71] Garisti G., Mitidieri E., “Nonexistence of positive solutions of quasilinear equations”, Adv. Diff. Equat., 2 (1997), 319–359 | MR

[72] Clement P., Manásevich R., Mitidieri E., “Positive solutions for a quasilinear system via blow-up”, Commun. Part. Diff. Eq., 18:12 (1993), 2071–2106 | DOI | MR | Zbl

[73] Deng K., Levin H. A., “The role of critical exponent in blow-up theorem”, J. Math. Anal. Appl., 243 (2000), 85–126 | DOI | MR | Zbl

[74] Egnell H., “Positive solutions of semilinear equations in cones”, Trans. Amer. Math. Soc., 330:1 (1992), 191–201 | DOI | MR | Zbl

[75] Egorov Yu. V., Galaktionov V. A., Kondratiev V. A., Pohozaev S. I., “On the necessary conditions of global existence of solutions to a quasilinear inequality in the half-space”, C. R. Acad. Sci. Paris. Ser. 1, 330 (2000), 93–98 | MR | Zbl

[76] Eidelman S. D., Kondratiev V. A., “Positive solutions of quasilinear Emden–Fowler systems of arbitrary order”, Russ. J. Math. Phys., 2:4 (1994), 535–540 | MR | Zbl

[77] Eidelman S. D., Kondratiev V. A., “On the summability in $L^p$ of positive solutions of elliptic equations”, Russ. J. Math. Phys., 7:2 (2000), 205–215 | MR

[78] Felmer P., de Figueiredo D. G., “Superquadratic elliptic systems”, Trans. Amer. Math. Soc., 343 (1994), 99–116 | DOI | MR | Zbl

[79] Filippucci R., Pucci P., “Nonexistence and other properties for solutions of quasilinear elliptic equations”, Diff. Integr. Eq., 8 (1995), 525–538 | MR | Zbl

[80] Furusho Y., Kusano T., Ogata A., “Symmetric positive entire solutions of second-order quasilinear degenerate elliptic equations”, Arch. Ration. Mech. Anal., 127 (1994), 231–254 | DOI | MR | Zbl

[81] Gallouët T., Morel J.-M., “Resolution of a semilinear equation in $L^1$”, Proc. Royal Soc. Edinburgh. Ser. A, 96 (1984), 275–288 | MR

[82] Galsina A., Mora X., Sola-Morales J., “The dynamical approach to elliptic problems in cylindrical domains and a study of their parabolic singular limit”, J. Differ. Equat., 102 (1993), 244–304 | DOI | MR

[83] Gidas B., Spruck J., “Global and local behavior of positive solutions of nonlinear elliptic equations”, Commun. Pure Appl. Math., 34 (1981), 525–598 | DOI | MR | Zbl

[84] Gidas B., Spruck J., “A priori bounds for positive solutions of nonlinear elliptic equations”, Commun. Part. Differ. Eq., 6:8 (1981), 883–901 | DOI | MR | Zbl

[85] Haviland E. K., “A note on unrestricted solutions of the differential equation $\Delta u=f(u)$”, J. London Math. Soc., 26 (1951), 210–214 | DOI | MR | Zbl

[86] Keller J. B., “On solutions of $\Delta u=f(u)$”, Commun. Pure Appl. Math., 10:4 (1957), 503–510 | DOI | MR | Zbl

[87] Kondratiev V. A., Oleinik O. A., “On asymptotic behavior of solutions of some nonlinear elliptic equations in unbounded domains”, Partial differential equations and related subjects, Pitman Research Notes in Math. Series, 269, Harlow, Longman, 1992, 163–195 | MR | Zbl

[88] Kondratiev V. A., Veron L., “Asymptotic behaviour of solutions of some nonlinear parabolic or elliptic equations”, Asymptotic Analysis, 14 (1997), 117–156 | MR | Zbl

[89] Kon'kov A. A., “Behavior of solutions of nonlinear second-order elliptic inequalities”, Nonlinear Analysis. Theory, Methods and Appl., 42:7 (2000), 1253–1270 | DOI | MR

[90] Kon'kov A. A., “On nonnegative solutions of quasilinear elliptic inequalities in domains belonging to $\mathbb R^2$”, Russ. J. Math. Phys., 7:4 (2000), 371–401 | MR

[91] Kuzin I., Pohozaev S., Entire solutions of semilinear elliptic equations, Progress in Nonlinear Differential Equations and their Applications, 33, Birkhäuser, Basel, 1997 | MR | Zbl

[92] Levine H. A., “The role of critical exponents in blowup problems”, SIAM Rev., 32 (1990), 262–288 | DOI | MR | Zbl

[93] Levine H. A., Payne L. E., “On the nonexistence of entire solutions to nonlinear second order elliptic equations”, SIAM. J. Math. Anal., 7:3 (1976), 337–343 | DOI | MR | Zbl

[94] Li Yi, Santanilla J., “Existence and nonexistence of positive singular solutions for semilinear elliptic problems with applications in astrophysics”, Differ. Integr. Equat., 8 (1995), 1369–1383 | MR | Zbl

[95] Littman W., Stampacchia G., Weinberger B., “Regular points for elliptic equations with discontinuous coefficients”, Ann. Scuola Norm. Super. Pisa. Ser. 3, 17:1–2 (1963), 43–77 | MR | Zbl

[96] Mitidieri E., “A Rellich type identity and applications”, Commun. Part. Diff. Eq., 18 (1993), 125–151 | DOI | MR | Zbl

[97] Mitidieri E., “Nonexistence of positive solutions of semilinear elliptic systems in $\mathbb R^n$”, Diff. Integr. Eq., 9 (1996), 465–479 | MR | Zbl

[98] Mitidiery E., Pohozaev S. I., “Nonexistence of weak solutions for some degenerate elliptic and parabolic problems on $\mathbb R^n$”, J. Evolut. Eq., 1 (2001), 189–220 | DOI | MR

[99] Moser J., “On Harnak's theorem for elliptic differential equations”, Commun. Pure Appl. Math., 14:3 (1961), 577–591 | DOI | MR | Zbl

[100] Ni W.-M., “On a singular elliptic equation”, Proc. Amer. Math. Soc., 88 (1983), 614–616 | DOI | MR | Zbl

[101] Ni W.-M., Serrin J., “Nonexistence theorems for quasilinear partial differential equations”, Rend. Circ. Mat. Palermo. Ser. 2. Suppl., 8 (1985), 171–185 | MR | Zbl

[102] Ni W.-M., Serrin J., “Nonexistence theorems for singular solutions of quasilinear partial differential equations”, Commun. Pure Appl. Math., 39 (1986), 379–399 | DOI | MR | Zbl

[103] Osserman R., On the inequality $\Delta u\geqslant f(u)$, Pacific J. Math., 7, no. 4, 1957 | MR | Zbl

[104] Redheffer R., “On entire solutions of nonlinear equations”, Bull. Amer. Math. Soc., 62 (1956), 408 pp. | MR | Zbl

[105] Reichel W., Zou H., “Nonexistence results for semilinear cooperative elliptic systems via moving spheres”, J. Diff. Eq., 161 (2000), 219–243 | DOI | MR | Zbl

[106] Sard A., “The measure of the critical values of differential maps”, Bull. Amer. Math. Soc., 48 (1942), 883–897 | DOI | MR

[107] Serrin J., Positive solutions of prescribed mean curvature problem, Lect. Notes Math., 1340, Springer, N.Y. etc., 1998

[108] Serrin J., Weinberger H. F., “Isolated singularities of solutions of linear elliptic equations”, Amer. J. Math., 88:1 (1966), 258–272 | DOI | MR | Zbl

[109] Serrin J., Zou H., “Nonexistence of positive solutions of Lane–Emden systems”, Diff. Integr. Eq., 9 (1996), 635–653 | MR | Zbl

[110] Serrin J., Zou H., “Existence of positive solutions of Lane–Emden systems”, Atti Sem. Mat. Fis. Univ. Modena, 46 (1998), 369–380 | MR | Zbl

[111] Serrin J., Zou H., “Symmetry of ground states of quasilinear elliptic equations”, Arch. Ration. Mech. Anal., 148 (1999), 265–290 | DOI | MR | Zbl

[112] Soranzo R., “Isolated singularities of positive solutions of superlinear biharmonic equations”, Potent. Anal., 6 (1997), 57–85 | DOI | MR | Zbl

[113] Stampacchia G., “Contributi alla regolarizzazione della soluzioni del problemi al contoro equazioni del secondo ordine ellitici”, Ann. Scu. Norm. Super. Pisa. Ser. 3, 12 (1958), 223–245 | MR | Zbl

[114] Stampacchia G., “Le probleme de Dirichlet pour les equations elliptique second ordre a coefficients discontinus”, Ann. Inst. Fourier, 15:1 (1965), 189–257 | MR | Zbl

[115] Trudinger N. S., “On Harnack type inequalities and their application to quasilinear elliptic equations”, Commun. Pure Appl. Math., 20 (1967), 721–744 | DOI | MR

[116] Vazques J. L., “Existence of solutions bounded at infinity for a semilinear elliptic equations on $\mathbb R^n$”, Select. Math., 31:1 (1980), 11–22 | MR

[117] Vazques J. L., “An a priori interior estimate for the solutions of a nonlinear problem representing weak diffusion”, Nonlinear Anal., 5 (1981), 95–103 | DOI | MR

[118] Vazques J. L., “On a semilinear equation in $\mathbb R^2$ involving bounded measures”, Proc. Roy. Soc. Edinburgh. Ser. A, 95 (1983), 181–202 | MR

[119] Vazques J. L., Veron L., “Singularities of elliptic equations with an exponential nonlinearity”, Math. Anal., 269 (1984), 119–135 | DOI | MR

[120] Vazques J. L., Veron L., “Isolated singularities of some semilinear elliptic equations”, J. Diff. Eq., 60 (1985), 301–322 | DOI | MR

[121] Veron L., “Solutions singuliere d'equations elliptiques semilineaires”, C. R. Acad. Sci. Ser. A, 288 (1979), 867–869 | MR | Zbl

[122] Veron L., “Singular solutions of some nonlinear elliptic equation”, Nonlinear Anal. Theory, Methods and Appl., 5:3 (1981), 225–242 | DOI | MR | Zbl

[123] Veron L., “Comportement asymptotique des solutions dKhequations elliptiques semilineaires dans $\mathbb R^n$”, Ann. Math. Pure Appl., 127 (1981), 25–50 | DOI | MR | Zbl

[124] Veron L., “Global behavior and symmetry properties of singular solutions of nonlinear elliptic equations”, Ann. Fac. Sci. Toulouse. Ser. 5, 6 (1984), 1–31 | MR | Zbl

[125] Veron L., Singularities of solutions of second order quasilinear equations, Pitman Res. Notes Math. Ser., 353, Longman, Harlow, 1996 | MR | Zbl

[126] Walter W., “Über ganze Lösungen der Differentialgleichung $\Delta u=f(u)$”, Über. Deutsch. Math. Verein., 57 (1955), 94–102 | MR | Zbl

[127] Wittich H., “Ganze Lösungen der Differentialgleichung $\Delta u=e^u$”, Math. Z., 49 (1944), 579–582 | DOI | MR | Zbl

[128] Yarur C., “Nonexistence of positive singular solutions for a class of semilinear elliptic systems”, J. Diff. Equat., 8 (1996), 1–22 | DOI | MR

[129] Zou H., “Symmetry of ground states of semilinear elliptic equations with mixed Sobolev growth”, Indiana Univ. Math. J., 45 (1996), 221–240 | DOI | MR | Zbl

[130] Zou H., “On positive solutions for semilinear elliptic equations with an indefinite nonlinearity via bifurcation”, J. Part. Diff. Eq., 13 (2000), 133–150 | MR | Zbl

[131] Zou H., “Symmetry of ground states for a semilinear elliptic system”, Trans. Amer. Math. Soc., 352 (2000), 1217–1245 | DOI | MR | Zbl