Existence and multiplicity of solutions for some second-order systems on time scales with impulsive effects

摘要

In this paper, we present a recent approach via variational methods and critical point theory to obtain the existence of solutions for the nonautonomous second-order system on time scales with impulsive effects { u Δ 2 ( t ) + A ( σ ( t ) ) u ( σ ( t ) ) + ? F ( σ ( t ) , u ( σ ( t ) ) ) = 0 , Δ -a.e. t ∈ [ 0 , T ] T κ ; u ( 0 ) ? u ( T ) = u Δ ( 0 ) ? u Δ ( T ) = 0 , ( u i ) Δ ( t j + ) ? ( u i ) Δ ( t j ? ) = I i j ( u i ( t j ) ) , i = 1 , 2 , … , N , j = 1 , 2 , … , p ,