Viability result for higher-order functional differential inclusions

Abstract

We prove, in separable Banach spaces, the existence of viable solutions for the following higher-order functional di erential inclusion x(t) \in F (t, T (t)x, x(t), ..., x(k 1)(t)), a.e. on [0, \tau ]. We consider the case when the right-hand side is nonconvex and the constraint is moving. „®¢®¤ ̈âìáï ÷á­ã¢ ­­ï ¢ ᥠ̄ à ¡¥«ì­ ̈å ¡ ­ 客 ̈å ̄à®áâ®à å ஧¢'ï§a÷¢ ­ ¢á쮬ã ÷­â¥à¢ «÷ ¤«ï äã­aæ÷®­ «ì­®-¤ ̈ä¥à¥­æ÷ «ì­ ̈å ¢a«î祭ì x(t) \in F (t, T (t)x, x(t), ..., x(k 1)(t)), a.e. on [0, \tau ]. ®§£«ï¤ õâìáï ¢ ̈ ̄ ¤®a ­¥® ̄ãa«®ù ̄à ¢®ù ç áâ ̈­ ̈ â àã宬®£® ®¡¬¥¦¥­­ï.