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

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Author(s): Nickolai Kosmatov

Journal: Electronic Journal of Differential Equations
ISSN 1072-6691

Volume: 2002;
Issue: 80;
Start page: 1;
Date: 2002;
Original page

Keywords: Sturm-Liouville problem | Green's function | fixed point theorem | Holder's inequality | multiple solutions.

ABSTRACT
We consider the Sturm-Liouville nonlinear boundary-value problem $$ displaylines{ -u''(t) = a(t)f(u(t)), quad 0 < t < 1, cr alpha u(0) - eta u'(0) =0, quad gamma u(1) + delta u'(1) = 0, } $$ where $alpha$, $eta$, $gamma$, $delta geq 0$, $alpha gamma + alpha delta + eta gamma > 0$ 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.
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