Positive solutions for a functional delay second-order three-point boundary-value problem

• Main Authors: Chuanzhi Bai, Xinya Xu
• Format: Article
• Language: English
• Published: Texas State University 2006-03-01
• Series: Electronic Journal of Differential Equations
• Subjects: Functional delay differential equation; boundary value problem; positive solutions; fixed point index.
• Online Access: http://ejde.math.txstate.edu/Volumes/2006/41/abstr.html
• ISSN: 1072-6691

We establish criteria for the existence of positive solutions to the three-point boundary-value problems expressed by second-order functional delay differential equations of the form $$displaylines{ - x''(t) = f(t, x(t), x(t - au), x_t), quad 0 <t< 1, cr x_0 = phi, quad x(1) = x(eta), }$$ where $phi in C[- au, 0]$, $0 < au < 1/4$, and $au < eta < 1$.