Geodesic
Positive solutions of a nonlinear higher order boundary-value problem
Electronic Journal of Differential Equations, Tome 2007 (2007).

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Summary: The authors consider the higher order boundary-value problem $$\displaylines{ u^{(n)}(t)= q(t)f(u(t)), \quad 0 \leq t \leq 1, \cr u^{(i-1)}(0) = u^{(n-2)}(p) = u^{(n-1)}(1)=0, \quad 1 \leq i \leq n-2, }$$ where $n\ge 4$ is an integer, and $p\in(1/2,1)$ is a constant. Sufficient conditions for the existence and nonexistence of positive solutions of this problem are obtained. The main results are illustrated with an example.
Classification : 34B18
Keywords: existence and nonexistence of positive solutions, guo-Krasnoselskii fixed point theorem, higher order boundary value problem 
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Graef, John R.; Henderson, Johnny; Yang, Bo. Positive solutions of a nonlinear higher order boundary-value problem. Electronic Journal of Differential Equations, Tome 2007 (2007). http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a123/