Geodesic
Liouville Theorems for Some Classes of Nonlinear Nonlocal Problems
Informatics and Automation, Studies on function theory and differential equations, Tome 248 (2005), pp. 164-184.

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This paper is devoted to the further development of the method of nonlinear capacity in the blow-up theory for nonlinear problems. In the framework of this approach, a new class of nonlinear problems with nonlocal nonlinearities is considered, including both stationary and evolution problems. Blow-up criteria depending on the structure of the nonlinear operator and the data of the problem under study are obtained. 
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E. Mitidieri; S. I. Pokhozhaev. Liouville Theorems for Some Classes of Nonlinear Nonlocal Problems. Informatics and Automation, Studies on function theory and differential equations, Tome 248 (2005), pp. 164-184. http://geodesic.mathdoc.fr/item/TRSPY_2005_248_a16/

[1] Akhmetov D.R., Lavrentiev M.M., Spigler R., “Existence and uniqueness of classical solutions to certain nonlinear integro-differential Fokker–Planck type equations”, El. J. Diff. Equat., 2002, no. 24 1–17 | MR

[2] Caristi G., Mitidieri E., “Existence and nonexistence of global solutions of higher-order parabolic problems with slow decay initial data”, J. Math. Anal. and Appl., 279 (2003), 710–722 | DOI | MR | Zbl

[3] D'Ambrosio L., Mitidieri E., Pohozaev S.I., “Representation formulae and inequalities for solutions of a class of second order partial differential equations”, Trans. Amer. Math. Soc., 358:2 (2006), 893–910 | DOI | MR | Zbl

[4] Fife P., “An integrodifferential analog of semilinear parabolic PDEs”, Partial differential equations and applications, Lect. Notes Pure and Appl. Math., 177, M. Dekker, New York, 1996, 137–145 | MR | Zbl

[5] Fife P., “Pattern formation in gradient systems”, Handbook in dynamical systems, v. 2, eds. B. Fiedler, G. Ioos, N. Kapel, Elsevier, Amsterdam, 2002, 677–722 | MR | Zbl

[6] Galaktionov V.A., Levine H.A., “A general approach to critical Fujita exponents in nonlinear parabolic problems”, Nonlin. Anal. Theory Meth. and Appl., 34:7 (1998), 1005–1027 | DOI | MR | Zbl

[7] Li Fu-Cai, Huang Shu-Xiang, Xie Chun-Hong, “Global existence and blow-up of solutions to a nonlocal reaction-diffusion system”, Discr. and Contin. Dyn. Syst., 9:6 (2003), 1519–1532 | DOI | MR | Zbl

[8] Li Yan Yan, “Remark on some conformally invariant integral equations: the method of moving spheres”, J. Europ. Math. Soc., 6 (2004), 153–180 | MR | Zbl

[9] Lieb E.H., Loss M., Analysis, 2nd ed., Grad. Stud. Math., 14, Amer. Math. Soc., Providence (RI), 2001 | MR | Zbl

[10] Mitidieri E., Pokhozhaev S.I., Apriornye otsenki i otsutstvie reshenii nelineinykh uravnenii i neravenstv v chastnykh proizvodnykh, Tr. MIAN, 234, Nauka, M., 2001

[11] Mitidieri E., Pokhozhaev S.I., “Svoistvo polozhitelnosti reshenii nekotorykh nelineinykh ellipticheskikh neravenstv v $\mathbb R^n$”, Dokl. RAN, 393:2 (2003), 159–164 | MR

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