Glasgow Mathematical Journal



MULTIPLE POSITIVE SOLUTIONS OF SINGULAR POSITONE DIRICHLET PROBLEMS WITH DERIVATIVE DEPENDENCE 1


BAOQIANG YAN a1, DONAL O'REGAN a2 and RAVI P. AGARWAL a3
a1 Department of Mathematics, Shandong Normal University, Ji-nan, 250014, P.R. China
a2 Department of Mathematics, National University of Ireland, Galway, Ireland
a3 Department of Mathematical Science, Florida Institute of Technology, Melbourne, Florida 32901, USA

Article author query
yan b   [Google Scholar] 
o'regan d   [Google Scholar] 
agarwal rp   [Google Scholar] 
 

Abstract

The existence of multiple positive solutions is presented for the singular Dirichlet boundary value problems \[\left\{\begin{array}{@{}ll} x^{\prime\prime}+\Phi(t)\,f(t,x(t),|x'(t)|)=0,\\[3pt] x(0)=0,\ \ x(1)=0, \end{array}\right.\] using the fixed point index; here $f$ may be singular at $x=0$ and $x'=0$.

(Published Online August 23 2006)
(Received November 4 2005)
(Revised February 3 2006)
(Accepted March 10 2006)



Footnotes

1 The project is supported by the fund of National Nature Science (10571111) and the fund of Natural Science of Shandong Province (Y2005A07).