Fractional Kirchhoff Hardy problems with weighted Choquard and singular nonlinearity
Date
2022-03-25
Authors
Sharma, Tarun
Goyal, Sarika
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article, we study the existence and multiplicity of solutions to the fractional Kirchhoff Hardy problem involving weighted Choquard and singular nonlinearity
M(‖u‖2) (-Δ)s u - γ u/|x|2s
= λl(x)u -q + 1/|x|α (∫Ω r(y)|u(y)|p/ |y|α|x-y|μ dy) r(x)|u|p-2u in Ω,
u > 0 in Ω, u = 0 in ℝN \ Ω,
where Ω ⊆ ℝN is an open bounded domain with smooth boundary containing 0 in its interior, N > 2s with s ∈ (0, 1), 0 < q < 1, 0 < μ < N, γ and λ are positive parameters, θ ∈ [1, p) with 1 < p < 2*μ,s,α, where 2*μ,s,α is the upper critical exponent in the sense of weighted Hardy-Littlewood-Sobolev inequality. Moreover M models a Kirchhoff coefficient, l is a positive weight
and r is a sign-changing function. Under the suitable assumption on l and r, we established the existence of two positive solutions to the above problem by Nehari-manifold and fibering map analysis with respect to the parameters.The
results obtained here are new even for s = 1.
Description
Keywords
Fractional Kirchhoff Hardy operator, Singular nonlinearity, Weighted Choquard type nonlinearity, Nehari-manifold, Fibering map
Citation
Sharma, T., & Goyal, S. (2022). Fractional Kirchhoff Hardy problems with weighted Choquard and singular nonlinearity. <i>Electronic Journal of Differential Equations, 2022</i>(25), pp. 1-29.
Rights
Attribution 4.0 International