Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 158, pp. 1-??.

Title: Positive solutions for boundary-value problems with integral
       boundary conditions on infinite intervals

Authors: Changlong Yu (Hebei Univ. of Science and Tech., China)
         Jufang Wang  (Hebei Univ. of Science and Tech., China)
	 Yanping Guo  (Hebei Univ. of Science and Tech., China)
	 Huixian Wei  (Shijiazhuang Inst. of Railway Tech., China)
	 
Abstract:
 In this article, we consider the existence of positive solutions
 for a class of boundary value problems with integral boundary conditions
 on infinite intervals
 $$\displaylines{
 (\varphi_{p}(x'(t)))'+\phi(t)f(t,x(t),x'(t))=0, \quad 0<t<+\infty,\cr
 x(0)=\int_0^{+\infty}g(s)x'(s)ds,\quad \lim_{t\to+\infty}x'(t)=0,
 }$$
 where $\varphi_{p}(s)=|s|^{p-2}s$, $p>1$. By applying the Avery-Peterson
 fixed point theorem in a cone, we obtain the existence of three positive
 solutions to the above boundary value problem and give an example at last. 

Submitted July 5, 2012. Published September 18, 2012.
Math Subject Classifications: 34B18, 34B15.
Key Words: Cone; Avery-Peterson fixed point theorem; positive solution; 
           integral boundary conditions; infinite interval.