Existence results for singular p-biharmonic problem with Hardy potential and critical Hardy-Sobolev exponent

2024/09/26 by Singh, Gurpreet
#35A15 #35B20 #35Q40 #35Q75 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2409.18041

Abstract

In this article, we consider the singular p-biharmonic problem involving Hardy potential and citical Hardy-Sobolev exponent. We study the existence of ground state solutions and least energy sign-changing solutions of the following problem Δ_p² u -λ₁ \frac|u|^p-2u|x|^2p= \frac|u|^p_*(α)-2|x|^αu+λ₂(|x|^-β*|u|^q)|u|^q-2u in \R^N, where p>2, 20, λ₂ ∈ \R, α, β∈ (0,N), p_*(α)=(p(N-α))/(N-2p) and N≥ 5. Firstly, we study existence of ground state solutions by using the minimization method on the associated Nehari manifold. Then, we investigate the least energy sign-changing solutions by considering the Nehari nodal set.

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