Geodesic
Semipositone $m$-point boundary-value problems
Electronic Journal of Differential Equations, Tome 2004 (2004).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 34B10, 34B18
Keywords: Green's function, fixed point theorem, positive solutions, multi-point boundary-value problem 
@article{EJDE_2004__2004__a111,
     author = {Kosmatov, Nickolai},
     title = {Semipositone $m$-point boundary-value problems},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2004},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a111/}
}
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Kosmatov, Nickolai. Semipositone $m$-point boundary-value problems. Electronic Journal of Differential Equations, Tome 2004 (2004). http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a111/