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Neutral functional differential and integrodifferential inclusions in Banach spaces

M. Benchohra, S. K. Ntouyas (2001)

Bollettino dell'Unione Matematica Italiana

In questo lavoro studiamo l'esistenza di soluzioni deboli su un intervallo compatto di problemi con valore iniziale per inclusioni funzionali neutre differenziali e integrodifferenziali in spazi di Banach. I risultati sono ottenuti usando un teorema di punto fisso per mappe condensanti dovuto a Martelli.

Noncompact perturbation of nonconvex noncompact sweeping process with delay

Mohammed S. Abdo, Ahmed G. Ibrahim, Satish K. Panchal (2020)

Commentationes Mathematicae Universitatis Carolinae

We prove an existence theorem of solutions for a nonconvex sweeping process with nonconvex noncompact perturbation in Hilbert space. We do not assume that the values of the orient field are compact.

Nonlinear boundary value problems for differential inclusions y'' ∈ F(t,y,y')

L. H. Erbe, W. Krawcewicz (1991)

Annales Polonici Mathematici

Applying the topological transversality method of Granas and the a priori bounds technique we prove some existence results for systems of differential inclusions of the form y'' ∈ F(t,y,y'), where F is a Carathéodory multifunction and y satisfies some nonlinear boundary conditions.

Nonlinear fractional differential inclusions with anti-periodic type integral boundary conditions

Bashir Ahmad, Sotiris K. Ntouyas (2012)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

This article studies a boundary value problem of nonlinear fractional differential inclusions with anti-periodic type integral boundary conditions. Some existence results are obtained via fixed point theorems. The cases of convex-valued and nonconvex-valued right hand sides are considered. Several new results appear as a special case of the results of this paper.

Nonlocal semilinear second-order differential inclusions in abstract spaces without compactness

Martina Pavlačková, Valentina Taddei (2023)

Archivum Mathematicum

We study the existence of a mild solution to the nonlocal initial value problem for semilinear second-order differential inclusions in abstract spaces. The result is obtained by combining the Kakutani fixed point theorem with the approximation solvability method and the weak topology. This combination enables getting the result without any requirements for compactness of the right-hand side or of the cosine family generated by the linear operator.

Numerical precision for differential inclusions with uniqueness

Jérôme Bastien, Michelle Schatzman (2002)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this article, we show the convergence of a class of numerical schemes for certain maximal monotone evolution systems; a by-product of this results is the existence of solutions in cases which had not been previously treated. The order of these schemes is 1 / 2 in general and 1 when the only non Lipschitz continuous term is the subdifferential of the indicatrix of a closed convex set. In the case of Prandtl’s rheological model, our estimates in maximum norm do not depend on spatial dimension.

Numerical precision for differential inclusions with uniqueness

Jérôme Bastien, Michelle Schatzman (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this article, we show the convergence of a class of numerical schemes for certain maximal monotone evolution systems; a by-product of this results is the existence of solutions in cases which had not been previously treated. The order of these schemes is 1/2 in general and 1 when the only non Lipschitz continuous term is the subdifferential of the indicatrix of a closed convex set. In the case of Prandtl's rheological model, our estimates in maximum norm do not depend on spatial dimension. ...

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