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.where Ω is an open bounded domain in R N with Lipschitz boundary, N > 2s, s ∈ (0, 1), γ ∈ (0, 1). We will employ variational techniques to show the existence of infinitely many weak solutions of the above problem.

On critical variable-order Kirchhoff type problems with variable singular exponent

“…Canino et al [8] generalized the result by Chen et al [10,Section 3] to the case of p-fractional Laplacian (−∆ p ) s . We draw the attention of the reader to [1,17] (not restricted to only these) for existence results and [15,29,30,36,38] for the multiplicity results. Off-late, from a scientific point of view, fractional Sobolev spaces and related non-local problems have attracted the attention of many scholars because they occur naturally in many fields, such as electrorheological fluids and image processing (cf.…”

Infinitely many small solutions to an elliptic PDE of variable exponent with a singular nonlinearity

“…What we can do is to direct the reader's attention to [10,11,12,13,14,15,16] and the references therein. The work due to [17] is the first of its kind that guarantees the existence of infinitely many positive solutions to a fractional Laplacian problem involving both a singularity and a power nonlinearity with constant exponent. The authors in [17] considered the following problem.…”