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.