An elliptic equation with no monotonicity condition on the nonlinearity
Department of Mathematics Embry-Riddle Aeronautical University Daytona Beach, Florida 32114-3900, USA; firstname.lastname@example.org
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.
Mathematics Subject Classification: 35J20 / 35J60
Key words: Mountain-pass theorem / variational methods / Nehari manifold / Brouwer degree / concentration-compactness.
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