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POSITIVE SOLUTIONS FOR NON-RESONANT SINGULAR BOUNDARY-VALUE PROBLEMS WITH A LINEAR TERM

Published online by Cambridge University Press:  09 February 2007

Haishen Lü ,
Donal O’Regan  and
Ravi P. Agarwal
Haishen Lü
Affiliation:
Department of Applied Mathematics, Hohai University, Nanjing 210098, China
Donal O’Regan
Affiliation:
Department of Mathematics, National University of Ireland, Galway, Ireland
Ravi P. Agarwal
Affiliation:
Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901-6975, USA (agarwal@fit.edu)
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Abstract

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This paper presents new existence results for the singular boundary-value problem

\begin{gather*} -u''+p(t)u=f(t,u),\quad t\in(0,1),\\ u(0)=0=u(1). \end{gather*}

In particular, our nonlinearity $f$ may be singular at $t=0,1$ and $u=0$.

Keywords

Primary 34B15non-resonant singular boundary-value problemspositive solutionupper and lower solution
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 50 , Issue 1 , February 2007 , pp. 217 - 228
Copyright
Copyright © Edinburgh Mathematical Society 2007