Positive solutions for three-point boundary value problems with dependence on the first order derivative

• Published in: Journal of mathematical analysis and applications Vol. 290; no. 1; pp. 291 - 301
• Main Authors: Guo, Yanping, Ge, Weigao
• Format: Journal Article
• Language: English
• Published: San Diego, CA Elsevier Inc 01-02-2004; Elsevier
• Subjects: Exact sciences and technology; Fixed point theorem in a cone; Green's function; Mathematical analysis; Mathematics; Partial differential equations; Positive solution; Sciences and techniques of general use; Three-point boundary value problem; Fixed point theorem in a cone; Green's function; Three-point boundary value problem; Positive solution; Cone; Fixed point theorem; Mathematical analysis; Differential equation; Existence of solution; Positive solution; Three point boundary value problem; Green function
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/j.jmaa.2003.09.061

A new fixed point theorem in a cone is applied to obtain the existence of at least one positive solution for the second order three-point boundary value problem
x″+f(t,x,x′)=0,
0<t<1,
x(0)=0,
x(1)=αx(η),
where
f is a nonnegative continuous function,
α>0,
η∈(0,1),
αη<1. The associated Green's function for the above problem is also used.