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 the variable-order fractional Laplacian operator, [u] s(.) is the Gagliardo seminorm and s(.) : R N × R N → (0, 1) is a continuous and symetric function. We assume that λ is a non-negative parameter , σ ≥ 1, m, q ∈ C(Ω) with 0 < m(x) < 1 < 2σ < q(x) < 2 * s(.) for all x ∈ Ω. We combine some variational techniques with a truncation argument in order to show the existence and the multiplicity of positive solutions for the above problem.