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Nonlinear evolution equations on locally closed graphs
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NETL
NSTL
Springer Nature
Let X be a real Banach space, let A: D(A) is contained in X → X be an m-dissipative operator, let / a nonempty, bounded interval and let K: I → D(A) be a given multi-valued function. By using the concept of A-quasi-tangent set introduced by Carja, Necula, Vrabie [8] and [9] and using a tangency condition expressed in the terms of this concept, we establish a necessary and sufficient condition for C~0-viability referring to nonlinear evolution inclusions of the form u'(t) ∈ Au(t) + F(t,u(t)), where F is a multi-function defined on the graph of K. As an application, we deduce a comparison result for a class of fully nonlinear evolution inclusions driven by multi-valued perturbations of subdifferentials.
NETL
NSTL
Springer Nature
