Nonlinear elliptic \(\mathrm{p}\)-Laplacian equations in the whole space. (English) Zbl 1533.35178
Summary: In this paper the existence and multiplicity of non-zero solutions for nonlinear Dirichlet problems involving the \(p\)-Laplacian operator and which are defined in the whole space is established. In particular, the existence of two non-zero solutions, one with negative energy and other with positive one for equations having combined effects of concave and convex nonlinearities is obtained. The approach is based on variational methods.
MSC:
| 35J92 | Quasilinear elliptic equations with \(p\)-Laplacian |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35A15 | Variational methods applied to PDEs |
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