Geodesic
Nontrivial solution for a three-point boundary-value problem
Electronic Journal of Differential Equations, Tome 2004 (2004).

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

Summary: In this paper, we study the existence of nontrivial solutions for the second-order three-point boundary-value problem $$\displaylines{ u''+f(t,u)=0,\quad 0 less than t less than 1, \cr u'(0)=0,\quad u(1)=\alpha u'(\eta). }$$ where $\eta \in (0,1), \alpha \in \mathbb{R}, f\in C([0,1]\times \mathbb{R},\mathbb{R})$. Under certain growth conditions on the nonlinearity $f$ and by using Leray-Schauder nonlinear alternative, sufficient conditions for the existence of nontrivial solution are obtained. We illustrate the results obtained with some examples.
Classification : 34B10, 34B15
Keywords: three-point boundary-value problem, nontrivial solution, Leray-Schauder nonlinear alternative 
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     author = {Sun, Yong-Ping},
     title = {Nontrivial solution for a three-point boundary-value problem},
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     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a3/}
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Sun, Yong-Ping. Nontrivial solution for a three-point boundary-value problem. Electronic Journal of Differential Equations, Tome 2004 (2004). http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a3/