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Existence to singular boundary value problems with sign changing nonlinearities using an approximation method approach. (English) Zbl 1164.34351
Summary: This paper studies the existence of solutions to the singular boundary value problem \[ \begin{cases} -u''=g(t,u)+h(t,u),\quad t\in (0,1),\\ u(0)=0=u(1), \end{cases} \] where \(g\:(0,1)\times (0,\infty )\to \mathbb R\) and \(h\:(0,1)\times [0,\infty )\to [0,\infty )\) 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.

34B16 Singular nonlinear boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
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