摘要：By applying the fixed point theorem in cones, some new and general results on the existence of positive solution to second order generalized Sturm-Liouville dynamical system on time scale T u 1 Δ Δ ( t ) + h 1 ( t ) f 1 ( t , u 1 ( t ) , u 2 ( t ) , u 1 Δ ( t ) , u 2 Δ ( t ) ) = 0 , u 2 Δ Δ ( t ) + h 2 ( t ) f 2 ( t , u 1 ( t ) , u 2 ( t ) , u 1 Δ ( t ) , u 2 Δ ( t ) ) = 0 , t ∈ [ t 1 , t 2 ] T , a u i ( t 1 ) - b u i Δ ( t 1 ) = ∑ k = 1 m - 2 a k u i ( ξ k ) , c u i ( σ ( t 2 ) ) + d u i Δ ( σ ( t 2 ) ) = ∑ k = 1 m - 2 b k u i ( ξ k ) , ( i = 1 , 2 ) , are obtained. The first-order Δ-derivatives are involved in the nonlinear terms explicitly. Mathematics Subject Classification (2000) 39A10
关键词：Sturm-Liouville dynamical system ; Cone ; Fixed point ; Positive solution ; Time scales
