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Article
An Elliptic Equation With No Monotonicity Condition on the Nonlinearity
ESAIM: Control, Optimisation and Calculus of Variations
(2006)
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 Theorem,
- variational methods,
- Nehari manifold,
- Brouwer degree,
- concentration-compactness
Disciplines
Publication Date
October, 2006
DOI
https://doi.org/10.1051/cocv:2006022
Citation Information
Gregory S. Spradlin. "An Elliptic Equation With No Monotonicity Condition on the Nonlinearity" ESAIM: Control, Optimisation and Calculus of Variations Vol. 12 Iss. 4 (2006) p. 786 - 794 ISSN: 1292-8119 Available at: http://works.bepress.com/greg_spradlin/7/