Geodesic
Positive solutions for semipositone fourth-order two-point boundary value problems
Electronic journal of differential equations, Tome 2007 (2007)
In this paper we investigate the existence of positive solutions of the following nonlinear semipositone fourth-order two-point boundary-value problem with second derivative:

$\displaylines{ u^{(4)}(t) = f(t, u(t), u''(t)), \quad 0 \leq t \leq 1, \cr u'(1) = u''(1) = u'''(1) = 0, \quad k u(0) = u'''(0), }$

where $-6 k 0, f \geq - M$, and $M$ is a positive constant. Our approach relies on the Krasnosel'skii fixed point theorem.
Classification : 34B16
Keywords: boundary value problem, positive solution, semipositone, fixed point 
@article{EJDE_2007__2007__a183,
     author = {Yang,  Dandan and Zhu,  Hongbo and Bai,  Chuanzhi},
     title = {Positive solutions for semipositone fourth-order two-point boundary value problems},
     journal = {Electronic journal of differential equations},
     year = {2007},
     volume = {2007},
     zbl = {1118.34019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a183/}
}
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Yang,  Dandan; Zhu,  Hongbo; Bai,  Chuanzhi. Positive solutions for semipositone fourth-order two-point boundary value problems. Electronic journal of differential equations, Tome 2007 (2007). http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a183/