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

Abstract

AbstractIn 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.Mathematics Subject Classification (2020): 35J2035J6035G3035J35Key words: Variable-order fractional Kirchhoff equationsingular problemvariational methodsimplicit function theorem