Radial solutions for the bilaplacian equation with vanishing or singular radial potentials

2018/06/04 by Marino Badiale, Badiale, Marino, Stefano Greco +3
Computer Science · Mathematics · #35J60 #35J91 (Primary) #46E35 (Secondary) #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1806.01311

openalex publication_date 2018/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given three measurable functions V(r )≥ 0, K(r)> 0 and Q(r )≥ 0, r>0, we consider the bilaplacian equation Δ² u+V(|x|)u=K(|x|)f(u)+Q(|x|) in ℝ^N and we find radial solutions thanks to compact embeddings of radial spaces of Sobolev functions into sum of weighted Lebesgue spaces.

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