Compactness and existence results in weighted Sobolev spaces of radial functions. Part II: Existence

2015/05/30 by Marino Badiale, Michela Guida, Sergio Rolando · 2 citations
Mathematics · #math.AP #msc:35J20 #msc:35J25 #msc:35J60 #msc:35Q55

paper · pdf · doi:10.1007/s00030-016-0411-0

published as Nonlinear Differential Equations and Applications NoDEA 23 (2016), 1-34 · 29 pages, 8 figures

arxiv created 2015/05/30 · arxiv updated 2016/12/08

Abstract

We prove existence and multiplicity results for finite energy solutions to the nonlinear elliptic equation -\triangle u+V( | x| ) u=g( | x| ,u) \textrmin Ω⊆ ℝ^N, N≥ 3, where Ω is a radial domain (bounded or unbounded) and u satisfies u=0 on ∂ Ω if Ω≠ ℝ^N and u→ 0 as | x| → ∞ if Ω is unbounded. The potential V may be vanishing or unbounded at zero or at infinity and the nonlinearity g may be superlinear or sublinear. If g is sublinear, the case with g( | ⋅ | ,0) ≠ 0 is also considered.

Cited by

• Compactness and existence results for the p-Laplace equation
• Radial solutions for the bilaplacian equation with vanishing or singular radial potentials

Related

• Radial nonlinear elliptic problems with singular or vanishing potentials
• Compactness and existence results in weighted Sobolev spaces of radial functions, Part I: Compactness
• Compactness and existence results for the p-Laplace equation
• Nonradial solutions of weighted elliptic superlinear problems in bounded symmetric domains
• Multiplicity and symmetry breaking for supercritical elliptic problems in exterior domains