Infinite horizon discrete time control problems for bounded processes.
Oscillations presque-périodiques forcées d'équations d'Euler-Lagrange
Almost periodic solutions of forced second order hamiltonian systems
Dependence results on almost periodic and almost automorphic solutions of evolution equations.
Sufficient conditions for infinite-horizon calculus of variations problems
Sufficient conditions for infinite-horizon calculus of variations problems
After a brief survey of the literature about sufficient conditions, we give different sufficient conditions of optimality for infinite-horizon calculus of variations problems in the general (non concave) case. Some sufficient conditions are obtained by extending to the infinite-horizon setting the techniques of extremal fields. Others are obtained in a special qcase of reduction to finite horizon. The last result uses auxiliary functions. We treat five notions of optimality. Our problems are essentially motivated...
Local attractivity in nonautonomous semilinear evolution equations
We study the local attractivity of mild solutions of equations in the form u’(t) = A(t)u(t) + f (t, u(t)), where A(t) are (possible) unbounded linear operators in a Banach space and where f is a (possible) nonlinear mapping. Under conditions of exponential stability of the linear part, we establish the local attractivity of various kinds of mild solutions. To obtain these results we provide several results on the Nemytskii operators on the space of the functions which converge to zero at infinity...
Euler-Lagrange equation for a delay variational problem
We establish Euler-Lagrange equations for a problem of Calculus of Variations where the unknown variable contains a term of delay on a segment
Resolvent of nonautonomous linear delay functional differential equations
The aim of this paper is to give a complete proof of the formula for the resolvent of a nonautonomous linear delay functional differential equations given in the book of Hale and Verduyn Lunel [9] under the assumption alone of the continuity of the right-hand side with respect to the time,when the notion of solution is a differentiable function at each point, which satisfies the equation at each point, and when the initial value is a continuous function.
On -Almost Periodic Solutions to Some Nonautonomous Differential Equations in Banach Spaces
In this paper we prove the existence and uniqueness of -almost periodic solutions to the nonautonomous ordinary differential equation , , where generates an exponentially stable family of operators and is a -almost periodic function with values in a Banach space . We also study a Volterra-like equation with a -almost periodic solution.
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