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POSITIVE SOLUTIONS OF NONLOCAL SINGULAR BOUNDARY VALUE PROBLEMS

Published online by Cambridge University Press:  11 October 2004

RAVI P. AGARWAL ,
DONAL O'REGAN  and
SVATOSLAV STANĚK
RAVI P. AGARWAL
Affiliation:
Department of Mathematical Sciences, Florida Institute of Technology Melbourne, Florida 32901-6975, USA e-mail: agarwal@fit.edu
DONAL O'REGAN
Affiliation:
Department of Mathematics, National University of Ireland, Galway, Ireland e-mail: donal.oregan@nuigalway.ie
SVATOSLAV STANĚK
Affiliation:
Department of Mathematical Analysis, Faculty of Science, Palacký University, Tomkova 40, 779 00 Olomouc, Czech Republic e-mail: stanek@risc.upol.cz
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Abstract

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The paper presents the existence result for positive solutions of the differential equation $(g(x))''=f(t,x,(g(x))')$ satisfying the nonlocal boundary conditions $x(0)=x(T)$, $\min\{ x(t): t \in J\}=0$. Here the positive function $f$ satisfies local Carathéodory conditions on $[0,T] \times (0,\infty) \times (\R {\setminus} \{0\})$ and $f$ may be singular at the value 0 of both its phase variables. Existence results are proved by Leray-Schauder degree theory and Vitali's convergence theorem.

Keywords

34B1634B15
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 46 , Issue 3 , September 2004 , pp. 537 - 550
Copyright
© 2004 Glasgow Mathematical Journal Trust