Équations différentielles -adiques. Croissance des solutions, factorisation, indice
Equations in differentials in the algebra of generalized stochastic processes
We consider an ordinary or stochastic nonlinear equation with generalized coefficients as an equation in differentials in the algebra of new generalized functions in the sense of [8]. Consequently, the solution of such an equation is a new generalized function. We formulate conditions under which the solution of a given equation in the algebra of new generalized functions is associated with an ordinary function or process. Moreover the class of all possible associated functions and processes is...
Equazioni differenziali ordinarie discontinue e stabilizzazione
Équilibre instable en régime semi-classique
Équilibre instable en régime semi-classique. II. Conditions de Bohr-Sommerfeld
Equilibria and strict equilibria of multivalued maps on noninvariant sets
This paper is concerned with existence of equilibrium of a set-valued map in a given compact subset of a finite-dimensional space. Previously known conditions ensuring existence of equilibrium imply that the set is either invariant or viable for the differential inclusion generated by the set-valued map. We obtain some equilibrium existence results with conditions which imply neither invariance nor viability of the given set. The problem of existence of strict equilibria is also discussed.
Equilibria of Runge-Kutta methods.
Equilibrium configurations and small oscillations of some dynamical systems
Equilibrium stability of a servo actuating flight controls in a servoelastic framework.
Equivalence and reduction of delay-differential systems
A new direct method is presented which reduces a given high-order representation of a control system with delays to a first-order form that is encountered in the study of neutral delay-differential systems. Using the polynomial system description (PMD) setting due to Rosenbrock, it is shown that the transformation connecting the original PMD with the first-order form is Fuhrmann's strict system equivalence. This type of system equivalence leaves the transfer function and other relevant structural...
Equivalence and symmetries of first order differential equations
In this article, the equivalence and symmetries of underdetermined differential equations and differential equations with deviations of the first order are considered with respect to the pseudogroup of transformations
Equivalence of differential equations and differential algebras
Equivalence of Functional-Differential Equations of Neutral Type and Abstract Cauchy Problems.
Equivalence of holonomic differential equations.
Equivalence of ill-posed dynamical systems
The problem of topological classification is fundamental in the study of dynamical systems. However, when we consider systems without well-posedness, it is unclear how to generalize the notion of equivalence. For example, when a system has trajectories distinguished only by parametrization, we cannot apply the usual definition of equivalence based on the phase space, which presupposes the uniqueness of trajectories. In this study, we formulate a notion of “topological equivalence” using the axiomatic...
Equivalent formulation and numerical analysis of a fire confinement problem
We consider a class of variational problems for differential inclusions, related to the control of wild fires. The area burned by the fire at time t> 0 is modelled as the reachable set for a differential inclusion ∈F(x), starting from an initial set R0. To block the fire, a barrier can be constructed progressively in time. For each t> 0, the portion of the wall constructed within time t is described by a rectifiable set γ(t) ⊂. In this paper we show that the search for blocking strategies...
Equivariant degree of convex-valued maps applied to set-valued BVP
An equivariant degree is defined for equivariant completely continuous multivalued vector fields with compact convex values. Then it is applied to obtain a result on existence of solutions to a second order BVP for differential inclusions carrying some symmetries.
Equivariant Hopf bifurcation in a ring of identical cells with delay.
Ergodic type solutions of differential equations with piecewise constant arguments.
Ergodicity and asymptotically almost periodic solutions of some differential equations.