Glasgow Mathematical Journal



POSITIVE SOLUTIONS OF NONLOCAL SINGULAR BOUNDARY VALUE PROBLEMS


RAVI P. AGARWAL a1, DONAL O'REGAN a2 and SVATOSLAV STANEK a3 1
a1 Department of Mathematical Sciences, Florida Institute of Technology Melbourne, Florida 32901-6975, USA e-mail: agarwal@fit.edu
a2 Department of Mathematics, National University of Ireland, Galway, Ireland e-mail: donal.oregan@nuigalway.ie
a3 Department of Mathematical Analysis, Faculty of Science, Palacký University, Tomkova 40, 779 00 Olomouc, Czech Republic e-mail: stanek@risc.upol.cz

Article author query
agarwal rp   [Google Scholar] 
o'regan d   [Google Scholar] 
stanek s   [Google Scholar] 
 

Abstract

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.

(Received October 3 2003)
(Accepted May 12 2004)

Maths Classification

34B16; 34B15.



Footnotes

1 Supported by grant no. 201/01/1451 of the Grant Agency of the Czech Republic and by the Council of the Czech Government J14/98:153100011.