We are interested in the problem of existence of soliton-like solutions for the nonlinear Klein-Gordon equation. In particular we study some necessary and sufficient conditions on the nonlinear term to obtain solitons of a given charge. We remark that the conditions we consider can be easily verified. Moreover we show that multiplicity of solitons of the same charge is guaranteed by the ``shape'' of the nonlinear term for equations on $\R^{N}$, hence without appealing to topological or geometrical properties of the domain.
Existence and multiplicity of stable bound states for the nonlinear Klein–Gordon equation
BONANNO, CLAUDIO
2010-01-01
Abstract
We are interested in the problem of existence of soliton-like solutions for the nonlinear Klein-Gordon equation. In particular we study some necessary and sufficient conditions on the nonlinear term to obtain solitons of a given charge. We remark that the conditions we consider can be easily verified. Moreover we show that multiplicity of solitons of the same charge is guaranteed by the ``shape'' of the nonlinear term for equations on $\R^{N}$, hence without appealing to topological or geometrical properties of the domain.File in questo prodotto:
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