Fractional Kirchhoff Hardy problems with weighted Choquard and singular nonlinearity




Sharma, Tarun
Goyal, Sarika

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Texas State University, Department of Mathematics


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.



Fractional Kirchhoff Hardy operator, Singular nonlinearity, Weighted Choquard type nonlinearity, Nehari-manifold, Fibering map


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.


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