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Nonlinear bound states outside an insulated sphere. (English) Zbl 0807.35134

The stability properties of the solitary waves of the nonlinear Schrödinger equation are studied. The solution satisfies a Neumann boundary condition on the sphere of radius \(R\). The nonlinear term is \(| u |^{p-1}u\) and, for instance, stability is found if \(p<1 + 4/n\) and \(R\) is sufficiently large \((x \in \mathbb{R}^ n)\).

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35B35 Stability in context of PDEs
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