Báo Cáo Báo cáo hóa học ON BOUNDARY VALUE PROBLEMS FOR SECOND-ORDER DISCRETE INCLUSIONS ´ PETR STEHLIK AND C

ON BOUNDARY VALUE PROBLEMS FOR SECOND-ORDER DISCRETE INCLUSIONS ´ PETR STEHLIK AND CHRISTOPHER C. TISDELL Received 8 October 2004 We prove some existence theorems regarding solutions to boundary value problems for systems of second-order discrete inclusions. For a certain class of right-hand sides, we present some lemmas showing that all solutions to discrete second-order inclusions satisfy an a priori bound. Then we apply these a priori bounds, in conjunction with an appropriate fixed point theorem for inclusions, to obtain the existence of solutions. The theory is highlighted with several examples. 1. Introduction The theory of differential inclusions has received much attention due to its versatility and generality. For example, differential inclusions can accurately model discontinuous processes, such as systems with dry friction; the work of an electric oscillator; and autopilot (and other) control systems [8]. When considering these (or other) situations in discrete time,