Weighted Choquard equation perturbed with weighted nonlocal term

2020/05/25 by Singh, Gurpreet
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2005.12001

Abstract

We investigate the following problem -\rm div(v(x)|∇ u|^m-2∇ u)+V(x)|u|^m-2u= (|x|^-θ*\frac|u|^b|x|^α)\frac|u|^b-2|x|^αu+λ(|x|^-γ*\frac|u|^c|x|^β)\frac|u|^c-2|x|^βu in \R^N, where b, c, α, β>0, θ,γ∈ (0,N), N≥ 3, 2≤ m< ∞ and λ∈ \R. Here, we are concerned with the existence of groundstate solutions and least energy sign-changing solutions and that will be done by using the minimization techniques on the associated Nehari manifold and the Nehari nodal set respectively.

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