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Nontrivial solutions of superlinear \(p\)-Laplacian equations. (English) Zbl 1161.35016

Summary: We consider \(p\)-Laplacian equations on a bounded domain, where the nonlinearity is superlinear but does not satisfy the usual Ambrosetti-Rabinowitz condition near infinity, or its dual version near zero. Nontrivial solutions are obtained by computing the critical groups and using Morse theory.

MSC:

35J60 Nonlinear elliptic equations
35J35 Variational methods for higher-order elliptic equations
35B38 Critical points of functionals in context of PDEs (e.g., energy functionals)
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