Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 135, pp. 1-17.

Title: Positive solutions for a system of second-order boundary-value 
       problems involving first-order derivatives

Authors: Kun Wang    (Qingdao Technological Univ., China)
         Zhilin Yang (Qingdao Technological Univ., China)

Abstract:
 In this article we study  the existence and multiplicity of positive
 solutions for the system of second-order boundary value problems
 involving first order derivatives
 $$\displaylines{
 -u''=f(t, u, u', v, v'),\cr
 -v''=g(t, u, u', v, v'),\cr
 u(0)=u'(1)=0,\quad v(0)=v'(1)=0.
 }$$
 Here $f,g\in C([0,1]\times \mathbb{R}_+^{4},
  \mathbb{R}_+)(\mathbb{R}_+:=[0,\infty))$.
 We use fixed point index theory to establish our main results based 
 on a priori  estimates achieved by utilizing Jensen's integral 
 inequality for concave functions and $\mathbb{R}_+^2$-monotone matrices.

Submitted May 31, 2012. Published August 17, 2012.
Math Subject Classifications: 34B18, 45G15, 45M20, 47H07, 47H11.
Key Words: System of second-order boundary-value problems;
           positive solution;  first-order derivative;
           fixed point index; R_+^2-monotone matrix; 
	   concave function.