Existence of two positive solutions for two kinds of fractional \(p\)-Laplacian equations
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.
scientific article; zbMATH DE number 7341750
scientific article