Document Type
Article
Publication/Presentation Date
10-2006
Abstract/Description
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.
Publication Title
ESAIM: Control, Optimisation and Calculus of Variations
DOI
https://doi.org/10.1051/cocv:2006022
Publisher
EDP Sciences
Required Publisher’s Statement
Publications in ESAIM-COCV are copyright protected, but distribution of copies for non-commercial use is allowed and encouraged. The original publication is available at www.esaim-cocv.org.
Scholarly Commons Citation
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
