Uniqueness for Boundary Value Problems for Second Order Finite Difference Equations

Maximum principles for second order dynamic equations on time scales

“…Our results unify and generalize the results of Mawhin, Tonkes and Thompson [7] and those given in Protter and Weinberger [8].…”

“…In this paper we establish time scales analogues of the results of [7] and [8] as well as analogues of other maximum principles. In a forthcoming paper we will apply these to obtain a priori bounds, uniqueness and oscillation results for boundary value problems for second order dynamic equations on time scales.…”

“…The basic strong maximum principle is as follows. Recently Mawhin, Tonkes and Thompson [7] established discrete analogues of the results of Protter and Weinberger and applied their results to answer some uniqueness questions posed in Thompson [10].…”

Applications of maximum principles to dynamic equations on time scales

“…Our results extend the continuous results given in Protter and Weinberger [14], and their discrete counterparts, see Agarwal [1] for general results, Agarwal et al [2] for oscillation results, Cheng [5] for alternative applications of maximum principles, and Mawhin et al [13] for non-linear comparisons, uniqueness results and approximations. The main contribution of this work consists in the fact that the presented results show the precise transition from the continuous to the discrete setting.…”

“…Recently, Mawhin et al [13] established discrete analogues of the strong maximum principle and its variants for ordinary differential equations (see Protter and Weinberger [14]). They applied their results to answer some uniqueness questions posed in Thompson [16].…”