## 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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### References:

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