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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
Affiliation: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 $f(t,u)$, 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)=0end {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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