Semiclassical Limit For the Nonlinear Klein Gordon Equation in Bounded Domains
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AbstractWe are interested in the existence of standing waves for the nonlinear Klein Gordon equation εWe want to use a Benci-Cerami type argument in order to prove a the existence of several standing waves localized in suitable points of D. The main result of this paper is that, under suitable growth condition on W, for ε suffciently small, we have at least cat(D) stationary solutions of equation (†), where cat(D) is the Ljusternik-Schnirelmann category. The proof is achieved by solving a constrained critical point problem via variational techniques.
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2013 ◽
Vol 22
(2)
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pp. 209-219
2020 ◽
Vol 484
(2)
◽
pp. 123723
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2007 ◽
Vol 38
(6)
◽
pp. 1912-1931
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