Proceedings of the Edinburgh Mathematical Society (Series 2)

Research Article

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

Haishen Lüa1, Donal O’Regana2 and Ravi P. Agarwala3

a1 Department of Applied Mathematics, Hohai University, Nanjing 210098, China

a2 Department of Mathematics, National University of Ireland, Galway, Ireland

a3 Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901-6975, USA (agarwal@fit.edu)

Abstract

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 $u=0$.

(Online publication February 09 2007)

(Received March 31 2005)

Keywords

  • Primary 34B15;
  • non-resonant singular boundary-value problems;
  • positive solution;
  • upper and lower solution