Necessary and Sufficient Conditions for Viability for Semilinear Differential Inclusions
نویسندگان
چکیده
Given a set K in a Banach space X, we define: the tangent set, and the quasi-tangent set to K at ξ ∈ K, concepts more general than the one of tangent vector introduced by Bouligand (1930) and Severi (1931). Both notions prove very suitable in the study of viability problems referring to differential inclusions. Namely, we establish several new necessary, and even necessary and sufficient conditions for viability referring to both differential inclusions and semilinear evolution inclusions, conditions expressed in terms of the tangency concepts introduced.
منابع مشابه
A Viability Result for Nonconvex Semilinear Functional Differential Inclusions
We establish some sufficient conditions in order that a given locally closed subset of a separable Banach space be a viable domain for a semilinear functional differential inclusion, using a tangency condition involving a semigroup generated by a linear operator.
متن کاملExistence Results on Random Impulsive Semilinear Functional Differential Inclusions with Delays
This article presents the result on existence of mild solutions for random impulsive semilinear functional differential inclusions under sufficient conditions. The results are obtained by using the Martelli fixed point theorem and the fixed point theorem due to Covitz and Nadler.
متن کاملOn controllability for nonconvex semilinear differential inclusions
We consider a semilinear differential inclusion and we obtain sufficient conditions for h-local controllability along a reference trajectory.
متن کاملNonlocal Controllability of Mixed Volterra-fredholm Type Fractional Semilinear Integro-differential Inclusions in Banach Spaces
In this paper, we establish a sufficient conditions for the nonlocal controllability of mixed VolterraFredholm type fractional semilinear integro-differential inclusions in Banach spaces. The results are obtained by using fractional calculus, operator semigroups and Bohnenblust-Karlin’s fixed point theorem. Finally, an example is given to illustrate the theoretical results.
متن کاملSemilinear nonlocal differential inclusions in Banach spaces
This paper is concerned with the existence of mild solutions to a class of semilinear differential inclusions with nonlocal conditions. By using the fixed point theory for multivalued maps, we get some general results on nonlocal differential inclusions, which include some recent results on nonlocal problems as special cases. An example of partial differential equations is provided to illustrat...
متن کامل