Existence of positive solutions for boundary value problem of second-order functional differential equation

Daquing Jiang, Northeast Normal University, Changchun, P. R. China
P. Weng, South China Normal University, Guangzhou, P. R. China

E. J. Qualitative Theory of Diff. Equ., No. 6. (1998), pp. 1-13.

Abstract: We use a fixed point index theorem in cones to study the existence of positive solutions for boundary value problems of second-order functional differential equations of the form $$\left\{ \begin{array}{ll} y''(x)+r(x)f(y(w(x)))=0,&0<x<1,\\ \alpha y(x)-\beta y'(x)=\xi (x),&a\leq x\leq 0,\\ \gamma y(x)+\delta y'(x)=\eta (x),&1\leq x\leq b; \end{array}\right.$$ where $w(x)$ is a continuous function defined on $[0,1]$ and $r(x)$ is allowed to have singularities on $[0,1]$. The result here is the generalization of a corresponding result for ordinary differential equations.

You can download the full text of this paper in DVI, PostScript or PDF format, or have a look at the Zentralblatt or the Mathematical Reviews entry of this paper.