Nodal solutions for singular second-order boundary-value problems

Benmezai, Abdelhamid ; Esserhane, Wassila ; Henderson, Johnny

Electronic journal of differential equations, Tome 2014 (2014)

Résumé

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.

Détail

Classification : 34B15, 34B16, 34B18
Keywords: singular second-order BVPs, nodal solutions, global bifurcation theorem