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 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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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     title = {Existence to singular boundary value problems with sign changing nonlinearities using an approximation method approach},
     journal = {Applications of Mathematics},
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     year = {2007},
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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

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