Positive solutions for a system of [formula omitted]-Laplacian boundary value problems

Abstract

This paper is concerned with the existence and multiplicity of positive solutions for the system of p -Laplacian boundary value problems − ( ( u i ′ ) p i − 1 ) ′ = f i ( t , u 1 , … , u n ) , u i ( 0 ) = u i ′ ( 1 ) = 0 , i = 1 , … , n , where n ⩾ 2 , p i > 1 , f i ∈ C ( [ 0 , 1 ] × R + n , R + ) ( i = 1 , … , n , R + : = [ 0 , ∞ ) ) . Based on a priori estimates achieved by utilizing the Jensen integral inequalities and R + n -monotone matrices, we use fixed point index theory to establish the existence and multiplicity of positive solutions for the above problem.