Multiplicity of solutions for variable-order fractional Kirchhoff problem with singular term

Abstract

In this paper, we consider a class of singular variable-order fractional Kirchhoff problem of the form: where is a bounded domain, is the variable-order fractional Laplacian operator, [u] s(·) is the Gagliardo seminorm and is a continuous and symmetric function. We assume that λ is a non-negative parameter, with and . We combine some variational techniques with a truncation argument in order to show the existence and the multiplicity of positive solutions to the above problem.