An elliptic PDE is studied which is a perturbation of an autonomousequation. The existence of a nontrivial solution is proven viavariational methods. The domain of the equation is unbounded, whichimposes a lack of compactness on the variational problem. In addition, a popular monotonicity condition on the nonlinearity is not assumed. Inan earlier paper with this assumption, a solution was obtained using asimple application of topological (Brouwer) degree. Here, a more subtledegree theory argument must be used.
