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Displaying 3881 –
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Etant donné un système différentiel linéaire de niveau unique quelconque, nous explicitons des formules donnant les multiplicateurs de Stokes en fonction de constantes de connexion dans le plan de Borel, généralisant ainsi les formules obtenues dans l’article Resurgence, Stokes phenomenon and alien derivatives for level-one linear differential systems (M. Loday-Richaud, P. Remy). Pour ce faire, nous nous ramenons à un système de niveaux par la méthode classique de réduction du rang ; puis, nous...
We consider some non-autonomous second order Cauchy problems of the form
ü + B(t)u̇ + A(t)u = f(t ∈ [0,T]), u(0) = u̇(0) = 0.
We assume that the first order problem
u̇ + B(t)u = f(t ∈ [0,T]), u(0) = 0,
has -maximal regularity. Then we establish -maximal regularity of the second order problem in situations when the domains of B(t₁) and A(t₂) always coincide, or when A(t) = κB(t).
We characterize existence and uniqueness of solutions for an inhomogeneous abstract delay equation in Hölder spaces. The main tool is the theory of operator-valued Fourier multipliers.
By using Fourier multiplier theorems we characterize the existence and uniqueness of periodic solutions for a class of second-order differential equations with infinite delay. We also establish maximal regularity results for the equations in various spaces. An example is provided to illustrate the applications of the results obtained.
We consider limit cycles of a class of polynomial differential systems of the form
where and are positive integers, and have degree and , respectively, for each , and is a small parameter. We obtain the maximum number of limit cycles that bifurcate from the periodic orbits of the linear center , using the averaging theory of first and second order.
This paper deals with the optimal control problem in which the controlled system is described by a fully coupled anticipated forward-backward stochastic differential delayed equation. The maximum principle for this problem is obtained under the assumption that the diffusion coefficient does not contain the control variables and the control domain is not necessarily convex. Both the necessary and sufficient conditions of optimality are proved. As illustrating examples, two kinds of linear quadratic...
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