Normalized solutions to a quasilinear equation involving critical Sobolev exponent

2024/12/16 by Nidhi Nidhi, Nidhi, K. Sreenadh +1 · 1 citation
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2412.11469

openalex publication_date 2024/12/16 · openalex created_date 2024/12/18 · openalex updated_date 2026/07/28

Abstract

In this paper we study the existence and regularity results of normalized solutions to the following quasilinear elliptic Choquard equation with critical Sobolev exponent and mixed diffusion type operators: -Δ_p u+(-Δ_p)^su · amp; = · amp; λ|u|^p-2u +|u|^{p^*-2}u+ μ(I_α*|u|^q)|u|^q-2u in ℝ^N, ∫_ℝ^N|u|^pdx · amp; = · amp; τ, where N≥ 3, τ>0, (p)/(2)((N+α)/(N))0 is a parameter, (-Δ_p)^s is the fractional p-laplacian operator, p^*=(Np)/(N-p) is the critical Sobolev exponent and λ appears as a Lagrange multiplier.

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• Pohožaev identity and the existence of normalized ground state solutions for variable exponent problems

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