Semiclassical limit for the nonlinear Klein Gordon equation in bounded domains
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.
math.AP↗