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Least energy solutions for elliptic equations in unbounded domains

Published online by Cambridge University Press:  14 November 2011

Manuel A. del Pino  and
Patricio L. Felmer
Manuel A. del Pino
Affiliation:
Department of Mathematics, University of Chicago, Chicago, Illinois 60637, U.S.A.
Patricio L. Felmer
Affiliation:
Departamento de Ing. Matemática F.C.F.M., Universidad de Chile, Casilla 170 Correo 3, Santiago, Chile
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Abstract

In this paper we study the existence of least energy solutions to subcritical semilinear elliptic equations of the form

where Ω is an unbounded domain in RN and f is a C1 function, with appropriate superlinear growth. We state general conditions on the domain Ω so that the associated functional has a nontrivial critical point, thus yielding a solution to the equation. Asymptotic results for domains stretched in one direction are also provided.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 1 , 1996 , pp. 195 - 208
Copyright
Copyright © Royal Society of Edinburgh 1996

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