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.
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