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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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