Existence of solutions for degenerate Kirchhoff type problems with fractional p-Laplacian

Abstract

<p>In this article, by using the Fountain theorem and Mountain pass theorem in critical point theory without Palais-Smale (PS) condition, we show the existence and multiplicity of solutions to the degenerate Kirchhoff type problem with the fractional p-Laplacian</p> <pre>(α + b ∫ ∫_ℝ^2N |u(x) - u(y)|^p / |x - y|^N+ps dx dy) (-∆)^s_pu = ƒ(x, u) in Ω,<br> u = 0 in ℝ^N \ Ω,</pre> <p>where (-∆)^s_p is the fractional p-Laplace operator with 0 < s < 1 < p < ∞, Ω is a smooth bounded domain of ℝ^N, N > 2s, α, b > 0 are constants and ƒ : Ω x ℝ → ℝ is a continuous function.</p>