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.


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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