Semipositone \(m\)-point boundary-value problems

Kosmatov, Nickolai

Electronic journal of differential equations, Tome 2004 (2004)

Résumé

We study the

$ \displaylines{ -[p(t)u'(t)]' = \lambda f(t,u(t)), \quad 0 less than t less than 1, \cr u'(0) = 0, \quad \sum_{i=1}^{m-2}\alpha_i u(\eta_i) = u(1), }$

where $\alpha_i$ for $1 \leq i \leq m-2$ and $\sum_{i=1}^{m-2}\alpha_i 1, m \geq 3$. We assume that $p(t)$ is non-increasing continuously differentiable on $(0,1)$ and $p(t)$ on $[0,1]$. Using a cone-theoretic approach we provide sufficient conditions on continuous $f(t,u)$ under which the problem admits a positive solution.

Détail

Classification : 34B10, 34B18
Keywords: Green's function, fixed point theorem, positive solutions, multi-point boundary-value problem