Electronic Journal of Differential Equations,
Vol. 2002(2002), No. 80, pp. 1-10.

Title: A note on the singular Sturm-Liouville  problem with infinitely
       many solutions

Author: Nickolai Kosmatov (Univ. Arkansas at Little Rock, Arkansas, USA)
         
Abstract: 
  We consider the Sturm-Liouville nonlinear boundary-value problem
  $$ \displaylines{ -u''(t) = a(t)f(u(t)), \quad 0 < t < 1, \cr
    \alpha u(0) - \beta u'(0) =0, \quad
    \gamma u(1) + \delta u'(1) = 0, }
  $$
  where $\alpha$, $\beta$, $\gamma$, $\delta \geq 0$,
  $\alpha \gamma + \alpha \delta + \beta \gamma > 0$
  and $a(t)$ is in a class of singular functions. Using a fixed point
  theorem we show that under certain growth conditions
  imposed on $f(u)$ the problem admits infinitely many solutions.
     
Submitted November 13, 2001. Published September 27, 2002.
Math Subject Classifications: 34B16, 34B18.
Key Words: Sturm-Liouville problem; Green's function;
           fixed point theorem;  Holder's inequality; 
           multiple solutions.