An elliptic equation with no monotonicity condition on the nonlinearity
ESAIM: Control, Optimisation and Calculus of Variations, Volume 12 (2006) no. 4, pp. 786-794.

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.

DOI: 10.1051/cocv:2006022
Classification: 35J20,  35J60
Keywords: mountain-pass theorem, variational methods, Nehari manifold, Brouwer degree, concentration-compactness
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Spradlin, Gregory S. An elliptic equation with no monotonicity condition on the nonlinearity. ESAIM: Control, Optimisation and Calculus of Variations, Volume 12 (2006) no. 4, pp. 786-794. doi : 10.1051/cocv:2006022. http://archive.numdam.org/articles/10.1051/cocv:2006022/

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