Mean-Periodic Solutions of Retarded Functional Differential Equations
In this paper we present a spectral criterion for existence of mean-periodic solutions of retarded functional differential equations with a time-independent main part.
Measure solutions for semilinear evolution equations with polynomial growth and their optimal control
In this paper we introduce a new concept of generalized solutions generalizing the notion of relaxed solutions recently introduced by Fattorini. We present some results on the question of existence of generalized or measure valued solutions for semilinear evolution equations on Banach spaces with polynomial nonlinearities. The results are illustrated by two examples one of which arises in nonlinear quantum mechanics. The results are then applied to some control problems.
Measure valued solutions for stochastic evolution equations on Hilbert space and their feedback control
In this paper, we consider a class of semilinear stochastic evolution equations on Hilbert space driven by a stochastic vector measure. The nonlinear terms are assumed to be merely continuous and bounded on bounded sets. We prove the existence of measure valued solutions generalizing some earlier results of the author. As a corollary, an existence result of a measure solution for a forward Kolmogorov equation with unbounded operator valued coefficients is obtained. The main result is further extended...
Measure valued solutions for systems governed by neutral differential equations on Banach spaces and their optimal control
In this paper we consider the question of existence of measure valued solutions for neutral differential equations on Banach spaces when there is no mild solutions. We prove the existence of measure solutions and their regularity properties. We consider also control problems of such systems and prove existence of optimal feedback controls for some interesting a-typical control problems.
Measure-differential inclusions in percussional dynamics.
Measures of noncompactness in the study of solutions of nonlinear differential and integral equations
The aim of this paper is to make an overview of some existence results for nonlinear differential and integral equations. Those results were obtained by the author and his co-workers during last years with some help of the technique of measures of noncompactness and a fixed point theorem of Darbo type.
Measuring the Irreversibility of Numerical Schemes for Reversible Stochastic Differential Equations
For a stationary Markov process the detailed balance condition is equivalent to the time-reversibility of the process. For stochastic differential equations (SDE’s), the time discretization of numerical schemes usually destroys the time-reversibility property. Despite an extensive literature on the numerical analysis for SDE’s, their stability properties, strong and/or weak error estimates, large deviations and infinite-time estimates, no quantitative results are known on the lack of reversibility...
Mechanical oscillators described by a system of differential-algebraic equations
The classical framework for studying the equations governing the motion of lumped parameter systems presumes one can provide expressions for the forces in terms of kinematical quantities for the individual constituents. This is not possible for a very large class of problems where one can only provide implicit relations between the forces and the kinematical quantities. In certain special cases, one can provide non-invertible expressions for a kinematical quantity in terms of the force, which then...
Mechanical oscillators with dampers defined by implicit constitutive relations
We study the vibrations of lumped parameter systems, the spring being defined by the classical linear constitutive relationship between the spring force and the elongation while the dashpot is described by a general implicit relationship between the damping force and the velocity. We prove global existence of solutions for the governing equations, and discuss conditions that the implicit relation satisfies that are sufficient for the uniqueness of solutions. We also present some counterexamples...
Media/psychological impact on multiple outbreaks of emerging infectious diseases.
Mellin analysis of singular and non-linear PDE's
Melnikov deviations and limit cycles for Lienard equations
Mémoire sur les équations différentielles linéaires
Meromorphic Solutions of Higher Order System of Algebraic Differential Equations.
Mesh Selection for Discrete Solution of Boundary Problems in Ordinary Differential Equations.
Mesoscopic morphology and scaling law of stationary interfacial patterns for reaction diffusion systems
Metastable aggregation within a discrete-time model.
Method of averaging for the system of functional-differential inclusions
The basic idea of this paper is to give the existence theorem and the method of averaging for the system of functional-differential inclusions of the form ⎧ (0) ⎨ ⎩ (1)
Method of lower and upper solutions for a generalized boundary value problem
Method of lower and upper solutions for a third-order three-point regular boundary value problem