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Existence and non-existence results for quasilinear elliptic exterior problems with nonlinear boundary conditions. (English) Zbl 1147.35038

Summary: Existence and non-existence results are established for quasilinear elliptic problems with nonlinear boundary conditions and lack of compactness. The proofs combine variational methods with the geometrical feature, due to the competition between the different growths of the nonlinearities.

MSC:

35J65 Nonlinear boundary value problems for linear elliptic equations
35J60 Nonlinear elliptic equations
35D05 Existence of generalized solutions of PDE (MSC2000)
35J35 Variational methods for higher-order elliptic equations
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
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References:

[1] Ambrosetti A., J. Funct. Anal. 14 pp 349– (1973) · Zbl 0273.49063 · doi:10.1016/0022-1236(73)90051-7
[2] Bahri A., Ann. Inst. H. Poincaré 14 pp 365– (1997) · Zbl 0883.35045 · doi:10.1016/S0294-1449(97)80142-4
[3] DiBenedetto E., Nonlinear Anal., Theory Methods Appl. 7 pp 827– (1983) · Zbl 0539.35027 · doi:10.1016/0362-546X(83)90061-5
[4] Gierer A., Kybernetik 12 pp 30– (1972) · doi:10.1007/BF00289234
[5] Keller E. F., J. Theor. Biol. 26 pp 399– (1970) · Zbl 1170.92306 · doi:10.1016/0022-5193(70)90092-5
[6] Pucci P., Handbook of Differential pp 355– (2007)
[7] Pucci P., Rend. Lincei Mat. Appl. 18 pp 257– (2007) · doi:10.1007/BF02934923
[8] Reed M., Methods of Modern Mathematical Physics IV. Analysis of Operators (1978) · Zbl 0401.47001
[9] Serrin J., Acta Math. 111 pp 247– (1964) · Zbl 0128.09101 · doi:10.1007/BF02391014
[10] Simon J., Journé es d’.Analyse Non Linéaire pp 205– (1978) · doi:10.1007/BFb0061807
[11] Strauss W. A., Comm. Math. Phys. 55 pp 149– (1977) · Zbl 0356.35028 · doi:10.1007/BF01626517
[12] Yu L. S., Proc. Amer. Math. Soc. 115 pp 1037– (1992)
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