The topological degree methods for the fractional \(p(\cdot)\)-Laplacian problems with discontinuous nonlinearities. (English. French summary) Zbl 1487.35400
Summary: In this article, we use the topological degree based on the abstract Hammerstein equation to investigate the existence of weak solutions for a class of elliptic Dirichlet boundary value problems involving the fractional \(p(x)\)-Laplacian operator with discontinuous nonlinearities. The appropriate functional framework for this problems is the fractional Sobolev space with variable exponent.
MSC:
| 35R11 | Fractional partial differential equations |
| 35A16 | Topological and monotonicity methods applied to PDEs |
| 35J25 | Boundary value problems for second-order elliptic equations |
| 35J92 | Quasilinear elliptic equations with \(p\)-Laplacian |
| 47H11 | Degree theory for nonlinear operators |
Keywords:
fractional \(p(x)\)-Laplacian; weak solution; discontinuous nonlinearity; topological degree theoryReferences:
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