Singular boundary value problems via the Conley index
Keywords
Singular boundary value problems, Conley indexAbstract
We use Conley index theory to solve the singular boundary value problem $\varepsilon^2D u_{xx} + f(u,\varepsilon u_x,x) = 0$ on an interval $[-1,1]$, where $u \in \mathbb R^n$ and $D$ is a diagonal matrix, with separated boundary conditions. Since we use topological methods the assumptions we need are weaker then the standard set of assumptions. The Conley index theory is used here not for detection of an invariant set, but for tracking certain cohomological information, which guarantees existence of a solution to the boundary value problem.Downloads
Published
2006-12-01
How to Cite
1.
GEDEON, Tomáš and MISCHAIKOW, Konstantin. Singular boundary value problems via the Conley index. Topological Methods in Nonlinear Analysis. Online. 1 December 2006. Vol. 28, no. 2, pp. 263 - 283. [Accessed 26 April 2024].
Issue
Section
Articles
Stats
Number of views and downloads: 0
Number of citations: 0