Positive solutions of a system of second order boundary value problems involving first order derivatives via [formula omitted]-monotone matrices

Abstract

In this paper we study the existence and multiplicity of positive solutions for the system of second order boundary value problems for nonlinear ordinary differential equations depending on first-order derivatives: − u i ′ ′ = f i ( t , u 1 , u 1 ′ , … , u n , u n ′ ) , u i ( 0 ) = u i ′ ( 1 ) = 0 , i = 1 , … , n . Here n ⩾ 2 , f i ∈ C ( [ 0 , 1 ] × R + 2 n , R + ) ( R + : = [ 0 , + ∞ ) ) . Based on a priori estimates achieved by using integral inequalities and R + n -monotone matrices, we use fixed point index theory to establish our main results for the above problem.