Abstract
The singular boundary-value problem$$ \left\{ {\begin{array}{*{20}{c}} {{u^{\prime\prime}} + g\left( {t,u,{u^{\prime}}} \right) = 0\quad {\text{for}}\quad t \in \left( {0,1} \right),} \hfill \\ {u(0) = u(1) = 0} \hfill \\ \end{array} } \right. $$is studied. The singularity may appear at u = 0, and the function g may change sign. An existence theorem for solutions to the above boundary-value problem is proposed, and it is proved via the method of upper and lower solutions.
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