Abstract
AbstractThe aim of this paper is to study the existence and multiplicity of solutions for a class of fractional Kirchho problems involving Choquard type nonlinearity and singular nonlinearity. Under suitable assumptions, two nonnegative and nontrivial solutions are obtained by using the Nehari manifold approach combined with the Hardy-Littlehood-Sobolev inequality.
Highlights
In this paper, we study the following Choquard-Kirchho problem involving singular nonlinearity: L(u) = λ f (x) uβ +g(y)|u(y)|q |x − y|μ d y g(x)u q− in RN, (1.1) RN u >in RN, where N ≥, < p < N/s with s ∈ (, ), < q < p*μ,s andL(u) = a + b[u](sθ,p− )p (−∆)sp u with a >, b ≥, θ ∈ [, q) and [u]s,p =
The aim of this paper is to study the existence and multiplicity of solutions for a class of fractional Kirchho problems involving Choquard type nonlinearity and singular nonlinearity
Two nonnegative and nontrivial solutions are obtained by using the Nehari manifold approach combined with the Hardy-Littlehood-Sobolev inequality
Summary
Xiang and Zhang in [41] discussed the following Schrödinger-Choquard-Kirchho type fractional p−Laplacian equations with upper critical exponents. In [12], Fiscella and Mishra studied the following Kirchho problem involving singular and critical nonlinearities λ f (x) uq. When λ is small enough, the authors obtained the existence of two positive solutions by using Nehari manifold method. Goel and Sreenadh [16] used the similar method as in [12] to discuss the following critical Choquard-Kirchho type problem. We are interested in the multiplicity of solutions for fractional Kirchho equations with Choquard and singular nonlinearities. Equation (1.1) is di erent from the problems considered in the literature, since (1.1) deals with fractional p-Kirchho equations with Choquard type and singular nonlinearities.
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