Positive solutions of singularly perturbed nonlinear elliptic problem on Riemannian manifolds with boundary
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Remannian manifold with boundary, semiclassical limit, Lusternik-Schnirelmann categoryAbstrakt
Let $(M,g)$ be a smooth connected compact Riemannian manifold of finite dimension $n\geq 2$\ with a smooth boundary $\partial M$. We consider the problem $$ \cases -\varepsilon ^{2}\Delta _{g}u+u=|u|^{p-2}u,\quad u> 0 &\text{ on }M,\\ \displaystyle \frac{\partial u}{\partial \nu }=0 & \text{on }\partial M, \endcases $$ where $\nu $ is an exterior normal to $\partial M$. The number of solutions of this problem depends on the topological properties of the manifold. In particular we consider the Lusternik Schnirelmann category of the boundary.Pobrania
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2010-04-23
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GHIMENTI, Marco & MICHELETTI, Anna Maria. Positive solutions of singularly perturbed nonlinear elliptic problem on Riemannian manifolds with boundary. Topological Methods in Nonlinear Analysis [online]. 23 kwiecień 2010, T. 35, nr 2, s. 319–337. [udostępniono 22.7.2024].
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