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. © EDP Sciences, SMAI 2006.
ESAIM: Control, Optimisation and Calculus of Variations
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Spradlin, G. S. (2006). An Elliptic Equation with No Monotonicity Condition on the Nonlinearity. ESAIM: Control, Optimisation and Calculus of Variations, 12(4). https://doi.org/10.1051/cocv:2006022