Infinite time optimal control and periodicity

For smooth nonlinear systems

Decay rates of solutions to dissipative nonlinear evolution equations with ellipticity

In this paper, we study the global existence and the asymptotic behavior of the solutions to the Cauchy problem for the following nonlinear evolution equations with ellipticity and dissipative effects

Inertial Gradient-Like Dynamical System Controlled by a Stabilizing Term

Let H be a real Hilbert space and let be a function that we wish to minimize. For any potential and any control function which tends to zero as t+, we study the asymptotic behavior of the trajectories of the following dissipative system:

Asymptotic behaviour of linear evolutionary integral equations

The asymptotic behaviour of bounded solutions of evolutionary integral equations in a Banach spaceX

Construction of asymptotic solutions of linear singularly perturbed systems of second order with degeneracy

The paper discusses the asymptotic behavior of the general solution of a linear singularly perturbed system

On solutions of quasilinear wave equations with nonlinear damping terms

In this paper we consider the existence and asymptotic behavior of solutions of the following problem:

Hamilton-Jacobi equations having only action functions as solutions

Let L(x, v) be a Lagrangian which is convex and superlinear in the velocity variable v, and let H(x, p) be the associated Hamiltonian. Conditions are obtained under which every viscosity solution of the Hamilton-Jacobi equation

On transformations z(t) = y(ϕ(t)) of ordinary differential equations

The paper describes the general form of an ordinary differential equation of the order n + 1 (n 1) which allows a nontrivial global transformation consisting of the change of the independent variable. A result given by J. Aczél is generalized. A functional equation of the form where are given functions, is solved on .     

Malliavin Calculus for White Noise Driven Parabolic SPDEs

We consider the parabolic SPDE

Vibrations of Elastic Strings: Mathematical Aspects, Part Two

Dedicated to Professor Jacque-Louis Lions on the occasion of his 70th birthday We consider a mixed problem for the operator

Approximate controllability for trajectories of a delay Volterra control system

For the abstract delay Volterra control system,

Construction of a solution of a mixed problem for the generalized heat conduction equation by the fourier method

By the Fourier method a solution of the equation

On the global bifurcation for a class of degenerate equations

We consider the nonlinear Dirichlet boundary value problems for the second order equation

L ∞-solutions for some nonlinear degenerate elliptic and parabolic equations

In this paper we prove the existence of bounded solutions for equations whose prototype is:

On the existence of periodic solutions for the equation\ddot x + f(x)\dot x + g(x) = 0

We establish in this work sufficient conditions for the existence of periodic solutions for the Liénard equation .     

Linear periodic control systems: Controllability with restrained controls

Consider the problem of null-controllability for a linear non-autonomous system of the form , whereX andU are Banach spaces,A(t) andB(t) are linear bounded operators for eacht 0, and is a subset containing 0 (but not necessarily as an interior point). Some necessary and sufficient conditions for local and global null-controllability are proved whenA(·) andB(·) are periodic continuous functions. The proofs of the main results are based on discretization and on consideration of the corresponding linear discrete-time systems.     

A Generalized Measure Concentrated on a Closed Set of Measure Zero

When E is a closed set of measure zero in the dyadic group and the Walsh series satisfies

Differenzverfahren für Schwingungen mit trockener und zäher Reibung und für Regelungssysteme

Summary In the present article we show that the solutions of initial value problems in ordinary differential equations with discontinuous right-hand side can be approximated by a slight modification of the Euler-Cauchy method. The method is succesfully applied to and for some initial values. By a solution of a differential equation with discontinuous right-hand side we mean the concept given by A. F. Filippov.     

On the decomposition problem of stability for Volterra integrodifferential equations

In this paper, we discuss the problem of stability of Volterra integrodifferential equationwith the decompositionwhere andin which is an matrix of functionB continuous forin which is an matrix of functionscontinuous for 0≤S≤ t<∞.According to the decomposition theory of large scale system and with the help of Liapunovfunctional, we give a criterion for concluding that the zero solution of (2) (i.e. large scale system(1)) is uniformly asymptotically stable.We also discuss the large scale system with the decompositionand give a criterion for determining that the solutions of (4) (i.e. large scale system (3)) areuniformly bounded and uniformly ultimately bounded.Those criteria are of simple forms, easily checked and applied.