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Stability of a Class of Differential Inclusions
Dynamics and Control, 2001The stability of differential inclusions \(\dot x \in F(x)\), \(x\in \mathbb{R}^{n}\), is studied by using minorant and majorant mappings \(F^{-}\) and \(F^{+}\) both either heterotone or pseudoconcave such that \(F^{-}(x)\leq F(x)\leq F^{+}(x).\) The main results concern asymptotically stable absorbing sets and include the case of a single equilibrium
Diamond, P. M., Opoitsev, V.
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Attractors of Differential Inclusions and Their Approximation
Ukrainian Mathematical Journal, 2000Let \((H,\langle \cdot,\cdot \rangle)\) be a separable Hilbert space, \(\varphi :H \mapsto(-\infty,\infty]\) be a proper, convex lower semi-continuous function with the domain \(D(\varphi)\), and \(\partial \varphi:D(\partial \varphi)\subset H \mapsto 2^H\) be the subdifferential of this function.
Kapustyan, O. V., Valero, J.
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Evolution Integro-Differential Inclusions
Set-Valued and Variational AnalysisIn this paper, authors provided existence and uniqueness results of local/global solution for a new evolution inclusion governed by the subdifferential of a function \(\varphi\) perturbed both by a Carathéodory mapping and by an integral forcing term.
Abderrahim Bouach +2 more
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On a Fractional Differential Inclusion with “Maxima”
Fractional Calculus and Applied Analysis, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Viability criteria for differential inclusions
Journal of Systems Science and Complexity, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Discrete approximations of differential inclusions.
Summary: This paper is devoted to discretization methods for initial value problems for differential inclusions. The main emphasis is on set-valued analogues of Runge-Kutta methods. The material is presented as a survey, simultaneously containing a series of new results. Complete proofs are contained in our extended version [Bayreuther Math. Schr.Lempio, Frank, Veliov, Vladimir
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On differential inclusions with an advanced argument
1992A differential inclusion with an advanced argument, \[ x'(t)\in F(t,x(t),x(\nu(t))),\tag{1} \] is considered in a separable, reflexive Banach space \(X\). It is assumed that \(\nu(t)\geq t\). The set-valued map \(F\) has non- empty compact convex values and it is \({\mathcal L}\times {\mathcal B}(X\times X)\)-measurable and upper semicontinuous on \(X ...
Kaczor, Wiesława (1949- ) +1 more
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