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Superlinear problems without Ambrosetti and Rabinowitz growth condition. (English) Zbl 1158.35400

Summary: Superlinear elliptic boundary value problems without Ambrosetti and Rabinowitz growth condition are considered. Existence of nontrivial solution is established by combining some arguments used by Struwe and Tarantello and Schechter and Zou (also by Wang and Wei). Firstly, by using the mountain pass theorem due to Ambrosetti and Rabinowitz solution is constructed for almost every parameter \(\lambda \) by varying the parameter \(\lambda \). Then, the continuation of the solutions is considered.

MSC:

35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
35J20 Variational methods for second-order elliptic equations
35B38 Critical points of functionals in context of PDEs (e.g., energy functionals)
35B60 Continuation and prolongation of solutions to PDEs
35D05 Existence of generalized solutions of PDE (MSC2000)
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References:

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