Infinitely many large solutions to a variable order nonlocal singular equation

Abstract

The paper establishes the existence of infinitely many large energy solutions for a nonlocal elliptic problem involving a variable exponent fractional \(p(\cdot )\)-Laplacian and a singularity, provided a positive parameter incorporated in the problem is sufficiently small. A variational method can be implemented for an associated problem obtained by truncation related to the singularity. A comparison argument allows one to pass to the original singular problem.