Geodesic
Perturbations of quasilinear elliptic equations and Fredholm manifolds
Sbornik. Mathematics, Tome 58 (1987) no. 1, pp. 223-243 
M. I. Vishik; S. B. Kuksin. Perturbations of quasilinear elliptic equations and Fredholm manifolds. Sbornik. Mathematics, Tome 58 (1987) no. 1, pp. 223-243. http://geodesic.mathdoc.fr/item/SM_1987_58_1_a12/
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     title = {Perturbations of quasilinear elliptic equations and {Fredholm} manifolds},
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     year = {1987},
     volume = {58},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1987_58_1_a12/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

A number of new results are obtained on the asymptotic expansion of eigenvalues and eigenvectors of spectral problems for quasilinear elliptic equations, and a theorem is proved on the existence of a large number of solutions of equations containing a parameter. Bibliography: 14 titles.

[1] Krasnoselskii M. A., Topologicheskie metody v teorii nelineinykh integralnykh uravnenii, Gostekhizdat, M., 1956 | MR

[2] Nirenberg L., “Variational and topological methods in nonlinear problems”, Bull. Amer. Math. Soc., 4:3 (1981), 267–302 | DOI | MR | Zbl

[3] Ambrosetti A., Rabinowitz P., “Dual variational methods in critical point theory and applications”, Journ. Funct. Anal., 14:4 (1973), 349–381 | DOI | MR | Zbl

[4] Pokhozhaev S. I., “O sobstvennykh funktsiyakh uravneniya – $\Delta u+\lambda f(u)=0$”, DAN SSSR, 165:1 (1965), 36–39 | Zbl

[5] Sitnikova E. G., “Teorema o silnom nule dlya ellipticheskogo uravneniya vysokogo poryadka”, Matem. sb., 81(123) (1970), 376–397 | MR | Zbl

[6] Khermander L., Lineinye differentsialnye operatory s chastnymi proizvodnymi, Mir, M., 1965 | MR

[7] Vainberg M. M., Trenogin V. A., Teoriya vetvleniya resheniya nelineinykh uravnenii, Nauka, M., 1969 | MR

[8] Kelli D. L., Obschaya topologiya, 2-e izd., Nauka, M., 1981 | MR

[9] Krasnoselskii M. A., Zabreiko P. P., Pustylnik E. I., Sobolevskii P. E., Integralnye operatory v prostranstvakh summiruemykh funktsii, Nauka, M., 1966 | MR

[10] Borisovich Yu. G., Zvyagin V. G., Sapronov Yu. I., “Nelineinye fredgolmovy otobrazheniya i teoriya Lere–Shaudera”, UMN, 32:4 (1977), 3–54 | MR | Zbl

[11] Khirsh I., Differentsialnaya topologiya, Mir, M., 1979 | MR | Zbl

[12] Go Kh.-S., Gaussovskie mery v banakhovykh prostranstvakh, Mir, M., 1979

[13] Fučik S., Nečas J., “Ljusternik–Schnirelman theorem and nonlinear eigenvalue problems”, Mathematische Nachrichten, 53 (1972), 277–289 | DOI | MR

[14] Saut J. C, Temam R., “Generic Properties of Nonlinear Boundary Value Problems”, Comm. in Part. Diff. Eq, 4:3 (1979), 293–319 | DOI | MR | Zbl