This paper is concerned with the existence of viable or monotone solutions of a first order functional differential inclusion in a separable Banach space. We consider two cases with moving constraints.
We prove, in separable Banach spaces, the existence of viable solutions for the following higher-order functional dierential inclusion x (k) (t) \in F (t, T (t)x, x (1) (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 ¢ ᥯ à ¡¥«ì¨å ¡ 客¨å¯à®áâ®à å à® §¢'ï §ª÷¢ ¢á쮬ã ÷â¥à¢ «÷ ¤«ï äãªae÷® «ì®-¤¨ä¥à¥ae÷ «ì¨å ¢ª«îç¥ì x (k) (t) \in F (t, T (t)x, x (1) (t), ..., x (k-1) (t)), a.e. on [0, \tau ]. ® §£«ï¤ õâìáï ¢¨¯ ¤®ª ¥®¯ãª«®ù¯à ¢®ù ç á⨨â àã宬®£® ®¡¬¥¦¥ï. K , dened below, is locally compact.
In this paper we prove existence results for boundary value problems for higher-order differential inclusion x .n/ .t/ 2 F .t; x.t// with nonlocal boundary conditions, where F is a compact convex L 1-Carathéodory multifunction.
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