Nodal solutions for singular second-order boundary-value problems

• Main Authors: Abdelhamid Benmezai, Wassila Esserhane, Johnny Henderson
• Format: Article
• Language: English
• Published: Texas State University 2014-07-01
• Series: Electronic Journal of Differential Equations
• Subjects: Singular second-order BVPs; nodal solutions; global bifurcation theorem
• Online Access: http://ejde.math.txstate.edu/Volumes/2014/156/abstr.html

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.