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On Signorini problem for von Kármán equations. The case of angular domain

Jan Franců (1979)

Aplikace matematiky

The paper deals with the generalized Signorini problem. The used method of pseudomonotone semicoercive operator inequality is introduced in the paper by O. John. The existence result for smooth domains from the paper by O. John is extended to technically significant "angular" domains. The crucial point of the proof is the estimation of the nonlinear term which appears in the operator form of the problem. The substantial technical difficulties connected with non-smoothness of the boundary are overcome...

On some topological methods in theory of neutral type operator differential inclusions with applications to control systems

Mikhail Kamenskii, Valeri Obukhovskii, Jen-Chih Yao (2013)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We consider a neutral type operator differential inclusion and apply the topological degree theory for condensing multivalued maps to justify the question of existence of its periodic solution. By using the averaging method, we apply the abstract result to an inclusion with a small parameter. As example, we consider a delay control system with the distributed control.

On the density of extremal solutions of differential inclusions

F. S. De Blasi, G. Pianigiani (1992)

Annales Polonici Mathematici

An existence theorem for the cauchy problem (*) ẋ ∈ ext F(t,x), x(t₀) = x₀, in banach spaces is proved, under assumptions which exclude compactness. Moreover, a type of density of the solution set of (*) in the solution set of ẋ ∈ f(t,x), x(t₀) = x₀, is established. The results are obtained by using an improved version of the baire category method developed in [8]-[10].

On the maximality of the sum of two maximal monotone operators.

Hassan Riahi (1990)

Publicacions Matemàtiques

In this paper we deal with the maximal monotonicity of A + B when the two maximal monotone operators A and B defined in a Hilbert space X are satisfying the condition: Uλ ≥ 0 λ (dom B - dom A) is a closed linear subspace of X.

On the worst scenario method: a modified convergence theorem and its application to an uncertain differential equation

Petr Harasim (2008)

Applications of Mathematics

We propose a theoretical framework for solving a class of worst scenario problems. The existence of the worst scenario is proved through the convergence of a sequence of approximate worst scenarios. The main convergence theorem modifies and corrects the relevant results already published in literature. The theoretical framework is applied to a particular problem with an uncertain boundary value problem for a nonlinear ordinary differential equation with an uncertain coefficient.

On the worst scenario method: Application to a quasilinear elliptic 2D-problem with uncertain coefficients

Petr Harasim (2011)

Applications of Mathematics

We apply a theoretical framework for solving a class of worst scenario problems to a problem with a nonlinear partial differential equation. In contrast to the one-dimensional problem investigated by P. Harasim in Appl. Math. 53 (2008), No. 6, 583–598, the two-dimensional problem requires stronger assumptions restricting the admissible set to ensure the monotonicity of the nonlinear operator in the examined state problem, and, as a result, to show the existence and uniqueness of the state solution....

Currently displaying 161 – 180 of 266