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arXiv · 1012.5660

Semiclassical limit for the nonlinear Klein Gordon equation in bounded domains

Marco G. Ghimenti·Carlo R. Grisanti
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Abstract

We are interested to the existence of standing waves for the nonlinear Klein Gordon equation ε^2{\box}ψ + W'(ψ) = 0 in a bounded domain D. The main result of this paper is that, under suitable growth condition on W, for ε sufficiently small, we have at least cat(D) standing wavesfor the equation (†), while cat(D) is the Ljusternik-Schnirelmann category.

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Marco G. Ghimenti, Carlo R. Grisanti. 2010-12-27. Semiclassical limit for the nonlinear Klein Gordon equation in bounded domains. https://arxiv.org/abs/1012.5660

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