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MULTIPLE POSITIVE SOLUTIONS OF SINGULAR POSITONE DIRICHLET PROBLEMS WITH DERIVATIVE DEPENDENCE

Published online by Cambridge University Press:  23 August 2006

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

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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 $x'=0$.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 48 , Issue 2 , May 2006 , pp. 309 - 329
Copyright
2006 Glasgow Mathematical Journal Trust

Footnotes

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