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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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


Authors: Wei-Cheng Lian, Fu-Hsiang Wong and Cheh-Chih Yeh
Journal: Proc. Amer. Math. Soc. 124 (1996), 1117-1126
MSC (1991): Primary 34B15
DOI: https://doi.org/10.1090/S0002-9939-96-03403-X
MathSciNet review: 1328358
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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)=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.


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Additional Information

Wei-Cheng Lian
Affiliation: Department of Mathematics, National Central University, Chung-Li, 32054 Taiwan, Republic of China

Fu-Hsiang Wong
Affiliation: 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
Affiliation: Department of Mathematics, National Central University, Chung-Li, 32054 Taiwan, Republic of China
Email: Yeh@wangwei.math.ncu.edu.tw

DOI: https://doi.org/10.1090/S0002-9939-96-03403-X
Keywords: Boundary value problems, positive solution, operator equation, cone, fixed point
Received by editor(s): September 21, 1994
Dedicated: Dedicated to Professor Taro Yoshizawa on his $75$th birthday
Communicated by: Hal L. Smith
Article copyright: © Copyright 1996 American Mathematical Society