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An elliptic equation with no monotonicity condition on the nonlinearity

Gregory S. Spradlin — 2006

ESAIM: Control, Optimisation and Calculus of Variations

An elliptic PDE is studied which is a perturbation of an autonomous equation. The existence of a nontrivial solution is proven 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...

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