Electron. J. Diff. Equ., Vol. 2014 (2014), No. 156, pp. 1-39.

Nodal solutions for singular second-order boundary-value problems

Abdelhamid Benmezai, Wassila Esserhane, Johnny Henderson

Abstract:
We use a global bifurcation theorem to prove the existence of nodal solutions to the singular second-order two-point boundary-value problem
$$\displaylines{ -( pu') '(t)=f(t,u(t))\quad t\in ( \xi ,\eta) , \cr au(\xi )-b\lim_{t\to\xi} p(t)u'(t)=0, \cr cu(\eta )+d\lim_{t\to\eta} p(t)u'(t)=0, }$$
where $\xi ,\eta $, $a,b,c,d$ are real numbers with $\xi <\eta$, $a,b,c,d\geq 0$ , $p:( \xi ,\eta ) \to [ 0,+\infty) $ is a measurable function with $\int_{\xi }^{\eta }1/p(s)\,ds<\infty $ and $f:[ \xi ,\eta ] \times [ 0,+\infty) \to [ 0,+\infty ) $ is a Caratheodory function.

Submitted January 27, 2014. Published July 7, 2014.
Math Subject Classifications: 34B15, 34B16, 34B18.
Key Words: Singular second-order BVPs; nodal solutions; global bifurcation theorem.

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Abdelhamid Benmezai
Faculty of Mathematics, USTHB, Algiers, Algeria
email: aehbenmezai@gmail.com
Wassila Esserhane
Graduate School of Statistics and Applied Economics
P.O. Box 11, Doudou Mokhtar
Ben-Aknoun Algiers, Algeria
email: ewassila@gmail.com
Johnny Henderson
Department of Mathematics, Baylor University
Waco, Texas 76798-7328, USA
email: Johnny_Henderson@baylor.edu

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