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Topological properties of the solution set of a class of nonlinear evolutions inclusions

Nikolaos S. Papageorgiou (1997)

Czechoslovak Mathematical Journal

In the paper we study the topological structure of the solution set of a class of nonlinear evolution inclusions. First we show that it is nonempty and compact in certain function spaces and that it depends in an upper semicontinuous way on the initial condition. Then by strengthening the hypothesis on the orientor field F ( t , x ) , we are able to show that the solution set is in fact an R δ -set. Finally some applications to infinite dimensional control systems are also presented.

Trichotomy and bounded solutions of nonlinear differential equations

Mieczysław Cichoń (1994)

Mathematica Bohemica

The existence of bounded solutions for equations x ' = A ( t ) x + f ( t , x ) in Banach spaces is proved. We assume that the linear part is trichotomic and the perturbation f satisfies some conditions expressed in terms of measures of noncompactness.

Ulam Stabilities for Partial Impulsive Fractional Differential Equations

Saïd Abbas, Mouffak Benchohra, Juan J. Nieto (2014)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this paper we investigate the existence of solutions for the initial value problems (IVP for short), for a class of implicit impulsive hyperbolic differential equations by using the lower and upper solutions method combined with Schauder’s fixed point theorem.

Unconditional stability of difference formulas

Tomáš Roubíček (1983)

Aplikace matematiky

The paper concerns the solution of partial differential equations of evolution type by the finite difference method. The author discusses the general assumptions on the original equation as well as its discretization, which guarantee that the difference scheme is unconditionally stable, i.e. stable without any stability condition for the time-step. A new notion of the A n -acceptability of the integration formula is introduced and examples of such formulas are given. The results can be applied to ordinary...

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