Existence of two positive solutions for two kinds of fractional \(p\)-Laplacian equations. (English) Zbl 1462.35450
Summary: The aim of this paper is to investigate the existence of two positive solutions to subcritical and critical fractional integro-differential equations driven by a nonlocal operator \(\mathcal{L}_K^p\). Specifically, we get multiple solutions to the following fractional \(p\)-Laplacian equations with the help of fibering maps and Nehari manifold. \(\begin{cases} (-\Delta)_p^s u (x) = \lambda u^q +u^r, & u>0 \text{ in }\Omega, \\ u=0, & \text{in }\mathbb{R}^N \backslash \Omega \end{cases}\). Our results extend the previous results in some respects.
MSC:
| 35R11 | Fractional partial differential equations |
| 35R09 | Integro-partial differential equations |
| 35J92 | Quasilinear elliptic equations with \(p\)-Laplacian |
| 35J25 | Boundary value problems for second-order elliptic equations |
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