## 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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### References:

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