Existence of positive solutions of a superlinear boundary value problem with indefinite weight
Abstract
We deal with the existence of positive solutions for a two-point boundary value problem associated with the nonlinear second order equation $u''+a(x)g(u)=0$. The weight $a(x)$ is allowed to change its sign. We assume that the function $g\colon\mathopen{[}0,+\infty\mathclose{[}\to\mathbb{R}$ is continuous, $g(0)=0$ and satisfies suitable growth conditions, so as the case $g(s)=s^{p}$, with $p>1$, is covered. In particular we suppose that $g(s)/s$ is large near infinity, but we do not require that $g(s)$ is non-negative in a neighborhood of zero. Using a topological approach based on the Leray-Schauder degree we obtain a result of existence of at least a positive solution that improves previous existence theorems.
- Publication:
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arXiv e-prints
- Pub Date:
- March 2015
- DOI:
- arXiv:
- arXiv:1503.04583
- Bibcode:
- 2015arXiv150304583F
- Keywords:
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- Mathematics - Classical Analysis and ODEs;
- 34B18;
- 34B15
- E-Print:
- 12 pages, 4 PNG figures