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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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