Multiple solutions for the fractional \(p\)-Laplacian with jumping reactions. (English) Zbl 1504.35207
Summary: We study a nonlinear elliptic equation driven by the degenerate fractional \(p\)-Laplacian, with Dirichlet-type condition and a jumping reaction, i.e., \((p-1)\)-linear both at infinity and at zero but with different slopes crossing the principal eigenvalue. Under two different sets of hypotheses, entailing different types of asymmetry, we prove the existence of at least two nontrivial solutions. Our method is based on degree theory for monotone operators and nonlinear fractional spectral theory.
MSC:
| 35P30 | Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs |
| 35J92 | Quasilinear elliptic equations with \(p\)-Laplacian |
| 35R11 | Fractional partial differential equations |
| 47H11 | Degree theory for nonlinear operators |
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