Multiple solutions for a nonlinear Dirichlet problem driven by degenerate \(p\)-Laplacian. (English) Zbl 1520.35090
Summary: The paper develops a variational approach for a parametric quasilinear elliptic equation driven by degenerate \(p\)-Laplacian. Note that the use of variational methods allows to obtain multiple solutions. In particular, here, the existence of at least three solutions is established under an appropriate growth condition of the nonlinear term.
MSC:
| 35J92 | Quasilinear elliptic equations with \(p\)-Laplacian |
| 35J25 | Boundary value problems for second-order elliptic equations |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35A15 | Variational methods applied to PDEs |
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