Remarks on the Existence of Regularly Varying Solutions for Second Order Linear Differential Equations
Remarque sur la méthode de la variation de la constante généralisée
Remarque sur la stabilité dans le cas d'une équation linéaire à paramètre retardé avec une perturbation non linéaire
Repelling conditions for boundary sets using Liapunov-like functions. I. - Flow-invariance, terminal value problem and weak persistence
Representation of the set of mild solutions to the relaxed semilinear differential inclusion
We study the relation between the solutions set to a perturbed semilinear differential inclusion with nonconvex and non-Lipschitz right-hand side in a Banach space and the solutions set to the relaxed problem corresponding to the original one. We find the conditions under which the set of solutions for the relaxed problem coincides with the intersection of closures (in the space of continuous functions) of sets of δ-solutions to the original problem.
Representations of solutions of periodic second order linear differential equations.
Resolvents, integral equations, limit sets
In this paper we study a linear integral equation , its resolvent equation , the variation of parameters formula , and a perturbed equation. The kernel, , satisfies classical smoothness and sign conditions assumed in many real-world problems. We study the effects of perturbations of and also the limit sets of the resolvent. These results lead us to the study of nonlinear perturbations.
Resommation des series formelles. Solutions d'équations différentielles linéaires ordinaires du second ordre dans le champ complexe au voisinage de singularités irrégulières.
Restricted total stability and total attractivity.
Retracts, fixed point index and differential equations.
Some problems in differential equations evolve towards Topology from an analytical origin. Two such problems will be discussed: the existence of solutions asymptotic to the equilibrium and the stability of closed orbits of Hamiltonian systems. The theory of retracts and the fixed point index have become useful tools in the study of these questions.
Rigorous numerics for symmetric homoclinic orbits in reversible dynamical systems
We propose a new rigorous numerical technique to prove the existence of symmetric homoclinic orbits in reversible dynamical systems. The essential idea is to calculate Melnikov functions by the exponential dichotomy and the rigorous numerics. The algorithm of our method is explained in detail by dividing into four steps. An application to a two dimensional reversible system is also treated and the existence of a symmetric homoclinic orbit is rigorously verified as an example.
Rigorous results on the power expansions for the integrals of a hamiltonian system near an elliptic equilibrium point
Robust dynamic output feedback fault-tolerant control for Takagi-Sugeno fuzzy systems with interval time-varying delay via improved delay partitioning approach
This paper addresses the problem of robust fault-tolerant control design scheme for a class of Takagi-Sugeno fuzzy systems subject to interval time-varying delay and external disturbances. First, by using improved delay partitioning approach, a novel n-steps iterative learning fault estimation observer under H ∞ constraint is constructed to achieve estimation of actuator fault. Then, based on the online estimation information, a fuzzy dynamic output feedback fault-tolerant controller considered...
Robustness of decentralized control subject to nonlinear perturbation in the system dynamics
Roughness of -dichotomies under small perturbations in .
Second method of Lyapunov for stability of linear impulsive differential-difference equations with variable impulsive perturbations.
Second order differential equations with complex-valued coefficients
Second-order differential equations with asymptotically small dissipation and piecewise flat potentials.
Self similar solutions of generalized Burgers equation.
Semistability of motions and regular dependence of limit sets on points in general semi-sytems