Geodesic
Existence to singular boundary value problems with sign changing nonlinearities using an approximation method approach
Applications of Mathematics, Tome 52 (2007) no. 2, pp. 117-135.

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This paper studies the existence of solutions to the singular boundary value problem \[ \left\rbrace \begin{array}{ll}-u^{\prime \prime }=g(t,u)+h(t,u),\quad t\in (0,1) , u(0)=0=u(1), \end{array}\right.\] where $g\:(0,1)\times (0,\infty )\rightarrow \mathbb{R}$ and $h\:(0,1)\times [0,\infty )\rightarrow [0,\infty )$ are continuous. So our nonlinearity may be singular at $t=0,1$ and $u=0$ and, moreover, may change sign. The approach is based on an approximation method together with the theory of upper and lower solutions.
DOI : 10.1007/s10492-007-0006-5
Classification : 34B15, 34B16
Keywords: singular boundary value problem; positive solution; upper and lower solution 
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Lü, Haishen; O'Regan, Donal; Agarwal, Ravi P. Existence to singular boundary value problems with sign changing nonlinearities using an approximation method approach. Applications of Mathematics, Tome 52 (2007) no. 2, pp. 117-135. doi : 10.1007/s10492-007-0006-5. http://geodesic.mathdoc.fr/articles/10.1007/s10492-007-0006-5/

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