Solutions concentrating at curves for some singularly perturbed elliptic problems. (English. Abridged French version) Zbl 1081.35044
Summary: We study positive solutions of the equation \(-\varepsilon^2 \Delta u+u=u^p\), where \(p>1\) and \(\varepsilon >0\) is small, with Neumann boundary conditions in a three-dimensional domain \(\varOmega\). We prove the existence of solutions concentrating along some closed curve on \(\partial \varOmega\).
MSC:
| 35J65 | Nonlinear boundary value problems for linear elliptic equations |
| 35B25 | Singular perturbations in context of PDEs |
References:
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