Existence of solutions for degenerate Kirchhoff type problems with fractional p-Laplacian
Date
2017-04-27
Authors
Nyamoradi, Nemat
Zaidan, Lahib Ibrahim
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
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
(α + b ∫ ∫ℝ2N |u(x) - u(y)|p / |x - y|N+ps dx dy) (-∆)spu = ƒ(x, u) in Ω,
u = 0 in ℝN \ Ω,
where (-∆)sp is the fractional p-Laplace operator with 0 < s < 1 < p < ∞, Ω is a smooth bounded domain of ℝN, N > 2s, α, b > 0 are constants and ƒ : Ω x ℝ → ℝ is a continuous function.
Description
Keywords
Kirchhoff nonlocal operators, Fractional differential equations, Fountain theorem, Mountain Pass Theorem, Critical point theory
Citation
Nyamoradi, N., & Zaidan, L. I. (2017). Existence of solutions for degenerate Kirchhoff type problems with fractional p-Laplacian. <i>Electronic Journal of Differential Equations, 2017</i>(115), pp. 1-13.
Rights
Attribution 4.0 International