Multiple clustered layer solutions for semilinear Neumann problems on a ball

53Citations
Citations of this article
5Readers
Mendeley users who have this article in their library.

Abstract

We consider the following singularly perturbed Neumann problem {ε2Δu-u+f(u)=0 in Ω; u>0 in Ω and ∂u/∂ν=0 on ∂Ω, where Ω=B1(0) is the unit ball in Rn, ε>0 is a small parameter and f is superlinear. It is known that this problem has multiple solutions (spikes) concentrating at some points of Ω̄. In this paper, we prove the existence of radial solutions which concentrate at N spheres ∪j=1N{|x|=rjε}, where 1>r1ε>r 2ε>⋯>rNε are such that 1-r1ε∼εlog1/ε,r j-1ε-rjε∼εlog1/ ε,j=2,...,N. © 2004 Elsevier SAS. All rights reserved.

Cite

CITATION STYLE

APA

Malchiodi, A., Ni, W. M., & Wei, J. (2005). Multiple clustered layer solutions for semilinear Neumann problems on a ball. Annales de l’Institut Henri Poincare (C) Analyse Non Lineaire, 22(2), 143–163. https://doi.org/10.1016/j.anihpc.2004.05.003

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free