Hostname: page-component-7b9c58cd5d-sk4tg Total loading time: 0 Render date: 2025-03-15T14:53:29.282Z Has data issue: false hasContentIssue false

Multiple solutions for a non-homogeneous elliptic equation at the critical exponent

Published online by Cambridge University Press:  12 July 2007

Mónica Clapp
Affiliation:
Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, Ciudad Universitaria, 04510 México D.F., Mexico
Manuel Del Pino
Affiliation:
Departamento de Ingeniería Matemática and CMM, Universidad de Chile, Casilla 170 Correo 3, Santiago, Chile
Monica Musso
Affiliation:
Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi, 24-10129 Torino, Italy
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We consider the equation−Δu = |u|4/(N−2)u + εf(x) under zero Dirichlet boundary conditions in a bounded domain Ω in RN exhibiting certain symmetries, with f ≥ 0, f ≠ 0. In particular, we find that the number of sign-changing solutions goes to infinity for radially symmetric f, as ε → 0 if Ω is a ball. The same is true for the number of negative solutions if Ω is an annulus and the support of f is compact in Ω.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2004