Geodesic
Eigenvalues and symmetric positive solutions for a three-point boundary-value problem
Electronic journal of differential equations, Tome 2005 (2005)
In this paper, we consider the second-order three-point boundary-value problem

$\displaylines{ u''(t)+f(t,u,u',u'')=0,\quad 0\leq t\leq 1,\cr u(0)=u(1)=\alpha u(\eta). }$

Under suitable conditions and using Schauder fixed point theorem, we prove the existence of at least one symmetric positive solution. We also study the existence of positive eigenvalues for this problem. We emphasis the highest-order derivative occurs nonlinearly in our problem.
Classification : 34B10, 34B15
Keywords: symmetric positive solution, three-point boundary-value problem, Schauder fixed point theorem, eigenvalue 
@article{EJDE_2005__2005__a5,
     author = {Sun,  Yongping},
     title = {Eigenvalues and symmetric positive solutions for a three-point boundary-value problem},
     journal = {Electronic journal of differential equations},
     year = {2005},
     volume = {2005},
     zbl = {1093.34008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a5/}
}
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JO  - Electronic journal of differential equations
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%A Sun,  Yongping
%T Eigenvalues and symmetric positive solutions for a three-point boundary-value problem
%J Electronic journal of differential equations
%D 2005
%V 2005
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%F EJDE_2005__2005__a5
Sun,  Yongping. Eigenvalues and symmetric positive solutions for a three-point boundary-value problem. Electronic journal of differential equations, Tome 2005 (2005). http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a5/