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An existence principle for solutions to a singular boundary-value problems

Authors:	Shiyou Weng Haiyin Gao Daqing Jiang Xuezhang Hou

Institution:	1.General Course Department,Suzhou Vocational University,Suzhou,P. R. China;2.Science College, Applied Mathematics Department,Changchun University,Changchun,P. R. China;3.School of Mathematics and Statistics,Northeast Normal University,Changchun,P. R. China;4.Mathematics Department,Towson University,Baltimore,USA

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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