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.

Mathematics Subject Classification (2020):

• 35J20
• 35J60
• 35G30
• 35J35

Key words:

• Variable-order fractional Kirchhoff equation
• singular problem
• variational methods
• implicit function theorem