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Concentration of solutions for a singularly perturbed Neumann problem in non-smooth domains. (English) Zbl 1209.35040
Summary: We consider the equation $$- \varepsilon^{2}\Delta u+u=u^p$$ in a bounded domain $$\Omega \subset \mathbb R^3$$ with edges. We impose Neumann boundary conditions, assuming $$1<p<5$$, and prove concentration of solutions at suitable points of $$\partial \Omega$$ on the edges.

##### MSC:
 35J60 Nonlinear elliptic equations 35J25 Boundary value problems for second-order elliptic equations 35J67 Boundary values of solutions to elliptic equations and elliptic systems 35B25 Singular perturbations in context of PDEs 35A30 Geometric theory, characteristics, transformations in context of PDEs
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