Geodesic
Positive solutions for an m-point boundary-value problem
Electronic Journal of Differential Equations, Tome 2008 (2008).

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

Summary: In this paper, we obtain sufficient conditions for the existence of a positive solution, and infinitely many positive solutions, of the m-point boundary-value problem $$\displaylines{ x''(t) = f(t, x(t)), \quad 0 t 1, \cr x'(0) = 0, \quad x(1)=\sum_{i=1}^{m-2}\alpha _{i}x(\eta _{i})\,. }$$ Our main tools are the Guo-Krasnoselskii's fixed point theorem and the monotone iterative technique. We also show that the set of positive solutions is compact.
Classification : 34B07, 34B10, 34B18, 34B27
Keywords: multi-point boundary, positive solution, guo-Krasnoselskii fixed point theorem 
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     author = {Truong, Le Xuan and Ngoc, Le Thi Phuong and Long, Nguyen Thanh},
     title = {Positive solutions for an m-point boundary-value problem},
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     volume = {2008},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a81/}
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Truong, Le Xuan; Ngoc, Le Thi Phuong; Long, Nguyen Thanh. Positive solutions for an m-point boundary-value problem. Electronic Journal of Differential Equations, Tome 2008 (2008). http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a81/