POSITIVE SOLUTIONS FOR A SYSTEM OF SECOND-ORDER BOUNDARY-VALUE PROBLEMS INVOLVING FIRST-ORDER DERIVATIVES

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 -u '' = f(t, u, u', v, v'), -v '' = g(t, u, u', v, v'), u(0) = u'(1) = 0, v(0) = v'(1) = 0. Here f, g is an element of C([0, 1] x R-+(4), R+)(R+ := [0, infinity)). 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 R-+(2)-monotone matrices.