Existence of infinitely many solutions for a nonlocal elliptic PDE involving singularity

Abstract

In this article, we will prove the existence of infinitely many positive weak solutions to the following nonlocal elliptic PDE. \begin{align} (-Δ)^s u&= \fracλ{u^γ}+ f(x,u)~\text{in}~Ω,\nonumber u&=0~\text{in}~\mathbb{R}^N\setminusΩ,\nonumber \end{align} where $\Omega$ is an open bounded domain in ${\mathbb{R}}^N$ with Lipschitz boundary, $N>2s$, $s\in (0,1)$, $\gamma \in (0,1)$. We will employ variational techniques to show the existence of infinitely many weak solutions of the above problem.

16 pages

References in corpus (5)

• From the long jump random walk to the fractional Laplacian
• Multiplicity and Hölder regularity of solutions for a nonlocal elliptic PDE involving singularity
• Existence, Uniqueness of Positive Solution to a Fractional Laplacians with Singular Nonlinearity
• Existence of infinitely many solutions for a nonlocal elliptic PDE involving singularity
• Nontrivial solutions of superlinear nonlocal problems

Cited by in corpus (5)

• On critical variable-order Kirchhoff type problems with variable singular exponent
• Existence of infinitely many solutions for a nonlocal elliptic PDE involving singularity
• An existence result for singular fractional Kirchhoff-Schrödinger-Poisson system
• Existence of at least $k$ solutions to a fractional $p$-Kirchhoff problem involving singularity and critical exponent
• On subelliptic equations on stratified Lie groups driven by singular nonlinearity and weak $L^1$ data