Δ▽-type Maximum Principles For Second-order Linear And Nonlinear Operators On Time Scales And Applications

In this paper, we establish the maximum principle ni=1u?i i≥ 0,for x ∈ Λk k. if u attains its maximum M in DT, then u ≡ M, for elliptic operators on time scales, state several generalizations, and apply them to receive the uniqueness of the boundary value problems for linear and nonlinear equations, and obtain the lower and upper solutions for dynamic equations and so on. And also establish the maximum principle for parabolic operators on time scales, state several generalizations, and apply them to receive the uniqueness of the boundary value problems.