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On the existence of positive solutions of nonlinear second order differential equations

Authors:	Wei-Cheng Lian Fu-Hsiang Wong Cheh-Chih Yeh

Institution:	Department of Mathematics, National Central University, Chung-Li, 32054 Taiwan, Republic of China Fu-Hsiang Wong ; Department of Mathematics and Science, National Taipei Teacher's College, 134, Ho Ping e. Rd. Sec. 2, Taipei 10659, Taiwan, Republic of China Cheh-Chih Yeh ; Department of Mathematics, National Central University, Chung-Li, 32054 Taiwan, Republic of China

Abstract:	Under suitable conditions on , the boundary value problem $\begin{equation}\begin {cases} (E)~~ u'(t)+f(t,u(t))=0~~~~~\hbox {in}~~~~~(0,1), (BC) \begin {cases} \alpha u(0)-\beta u'(0)=0, \gamma u(1)+\delta u'(1)=0\end {cases} \end {cases} \tag {(BVP)} \end{equation*}$ has at least one positive solution. Moreover, we also apply this main result to establish several existence theorems of multiple positive solutions for some nonlinear (elliptic) differential equations.

Keywords:	Boundary value problems positive solution operator equation cone fixed point

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