Volume 12, Number 4, October 2006
|Page(s)||786 - 794|
|Published online||11 October 2006|
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.
© EDP Sciences, SMAI, 2006
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.