Positive solutions of singularly perturbed nonlinear elliptic problem on Riemannian manifolds with boundary
Keywords
Remannian manifold with boundary, semiclassical limit, Lusternik-Schnirelmann categoryAbstract
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.Downloads
Published
2010-04-23
How to Cite
1.
GHIMENTI, Marco and MICHELETTI, Anna Maria. Positive solutions of singularly perturbed nonlinear elliptic problem on Riemannian manifolds with boundary. Topological Methods in Nonlinear Analysis. Online. 23 April 2010. Vol. 35, no. 2, pp. 319 - 337. [Accessed 28 March 2024].
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