### 1 Déformations des structures de Poisson et formulation isospectrale des problèmes d'évolution non linéaires

Skip to main content (access key 's'),
Skip to navigation (access key 'n'),
Accessibility information (access key '0')

It is established convergence to a particular equilibrium for weak solutions of abstract linear equations of the second order in time associated with monotone operators with nontrivial kernel. Concerning nonlinear hyperbolic equations with monotone and conservative potentials, it is proved a general asymptotic convergence result in terms of weak and strong topologies of appropriate Hilbert spaces. It is also considered the stabilization of a particular equilibrium via the introduction of an asymptotically...

We consider evolution differential equations in Fréchet spaces with unconditional Schauder basis, and construct a version of the majorant functions method to obtain existence theorems for Cauchy problems. Applications to PDE are also considered.

The equation φ (x) = g(x,φ (x)) in spaces of real-analytic functions is considered. Connections between local and global aspects of its solvability are discussed.

This paper addresses the Cauchy problem for the gradient flow equation in a Hilbert space $\mathscr{H}$$$\left\{\begin{array}{c}{u}^{}\hfill \end{array}\right.$$

The recent development of mathematical methods of investigation of problems with hysteresis has shown that the structure of the hysteresis memory plays a substantial role. In this paper we characterize the hysteresis operators which exhibit a memory effect of the Preisach type (memory preserving operators). We investigate their properties (continuity, invertibility) and we establish some relations between special classes of such operators (Preisach, Ishlinskii and Nemytskii operators). For a general...

A model of a cable stayed bridge is proposed. This model describes the behaviour of the center span, the part between pylons, hung on one row of cable stays. The existence, the uniqueness of a solution of a time independent problem and the continuous dependence on data are proved. The existence and the uniqueness of a solution of a linearized dynamic problem are proved. A homogenizing procedure making it possible to replace cables by a continuous system is proposed. A nonlinear dynamic problem connected...

In this paper we introduce a new concept of generalized solutions generalizing the notion of relaxed solutions recently introduced by Fattorini. We present some results on the question of existence of generalized or measure valued solutions for semilinear evolution equations on Banach spaces with polynomial nonlinearities. The results are illustrated by two examples one of which arises in nonlinear quantum mechanics. The results are then applied to some control problems.

The existence of multiple solutions for perturbed equations is shown near a manifold of solutions of an unperturbed equation via the Nielsen fixed point theory.

In this paper we deal with the Cauchy problem for differential inclusions governed by $m$-accretive operators in general Banach spaces. We are interested in finding the sufficient conditions for the existence of integral solutions of the problem ${x}^{\text{'}}\left(t\right)\in -Ax\left(t\right)+f(t,x\left(t\right))$, $x\left(0\right)={x}_{0}$, where $A$ is an $m$-accretive operator, and $f$ is a continuous, but non-compact perturbation, satisfying some additional conditions.