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An elliptic equation with no monotonicity condition on the nonlinearity

Published online by Cambridge University Press:  11 October 2006

Gregory S. Spradlin
Gregory S. Spradlin*
Affiliation:
Department of Mathematics Embry-Riddle Aeronautical University Daytona Beach, Florida 32114-3900, USA; spradlig@erau.edu
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Abstract

An elliptic PDE is studied which is a perturbation of an autonomous equation. The existence of a nontrivial solution is proven via variational methods. The domain of the equation is unbounded, which imposes a lack of compactness on the variational problem. In addition, a popular monotonicity condition on the nonlinearity is not assumed. In an earlier paper with this assumption, a solution was obtained using a simple application of topological (Brouwer) degree. Here, a more subtle degree theory argument must be used.

Keywords

Mountain-pass theoremvariational methodsNehari manifoldBrouwer degreeconcentration-compactness.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 12 , Issue 4 , October 2006 , pp. 786 - 794
Copyright
© EDP Sciences, SMAI, 2006

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