Global behavior of the branch of positive solutions for nonlinear Sturm–Liouville problems
✍ Scribed by T. Shibata
- Publisher
- Springer
- Year
- 2006
- Tongue
- English
- Weight
- 196 KB
- Volume
- 186
- Category
- Article
- ISSN
- 0373-3114
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we are concerned with proving the existence of positive solutions of two-point boundary value problems for the nonlinear discrete Sturm-Liouville equation Z&(t) := -Ab(t -I)Az/(tl)] + q(t)y(t) = f(t, y(t)). We will use some results for differentiable operators along a certain cone in a Banach space.
In this paper, the following nonlinear Sturm-Liouville problem is discussed by topological methods. In the case that the nonlinear term is non-singular or singular, a global structure of the positive solution set of the above problem is obtained, and the existence of positive solutions is proved un