Semiclassical limit for the nonlinear Klein Gordon equation in bounded domains
Analysis of PDEs
2010-12-30 v1
Abstract
We are interested to the existence of standing waves for the nonlinear Klein Gordon equation {\epsilon}^2{\box}{\psi} + W'({\psi}) = 0 in a bounded domain D. The main result of this paper is that, under suitable growth condition on W, for {\epsilon} sufficiently small, we have at least cat(D) standing wavesfor the equation ({\dag}), while cat(D) is the Ljusternik-Schnirelmann category.
Keywords
Cite
@article{arxiv.1012.5660,
title = {Semiclassical limit for the nonlinear Klein Gordon equation in bounded domains},
author = {Marco G. Ghimenti and Carlo R. Grisanti},
journal= {arXiv preprint arXiv:1012.5660},
year = {2010}
}