Second-order viability result in Banach spaces

Viability result for higher-order functional differential inclusions

“…This work extends results which are presented in [1,2,3,4,5,8,12]. Indeed, we get an existence result, in a separable Banach space, for higher-order functional dierential inclusions, with a constraint which depends on time.…”

“…\leq H \Biggl( F (t, T (\theta n (t))x n , x (1) n (\theta n (t)), ..., x (k - 1) n (\theta n (t)))), F (t, T (t)z 0 , z 1 (t), ..., z k - 1 (t))…”

“…x(t) \in K, \forall t \in [0, \tau ], (1.2) where F is upper semi-continuous set valued-map with compact convex values and K is a set in E such that the graph of A (k - 1) Recently, in [1], Aitalioubrahim and Sajid have established the existence of viable solutions to (1.1), without memory, in Banach space when C is xed and F is integrably bounded, measurable with respect to the rst argument and Lipschitz continuous with respect to the third argument. In addition, they have considered the following tangential condition:…”

“…As is known, viability problems need tangential conditions. For the problem (1.1), we shall use a tangency condition which is weaker than that used in [3].…”