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Criterion for Lyapunov Reducibility of a Linear Autonomous Differential System to a Linear Autonomous Equation
AbstractWe establish a unified criterion for the reducibility of a linear homogeneous differential system with constant coefficients to a linear...
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Characterization of shadowing for linear autonomous delay differential equations
A well-known shadowing theorem for ordinary differential equations is generalized to delay differential equations. It is shown that a linear...
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Approximate and optimal controllability of a second order non-autonomous stochastic differential equation with deviated arguments
This paper studies a second-order non-autonomous stochastic differential equation with deviated arguments and nonlocal finite delay in a Hilbert...
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Pullback Exponential Attractors with Explicit Fractal Dimensions for Non-Autonomous Partial Functional Differential Equations
The aim of this paper is to propose a new method to construct pullback exponential attractors with explicit fractal dimensions for non-autonomous...
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Exponential Stability of Autonomous Differential Equations of Neutral Type. II
Abstract—Linear autonomous differential equations of neutral type are considered. Invertibility criteria for the operator at the derivative in the...
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Exponential Stability of Autonomous Differential Equations of Neutral Type. I
AbstractIn this paper the linear differential equations of neutral type are considered. The necessary and sufficient conditions are established under...
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Orbital Stability of Small Periodic Solutions of an Autonomous System of Differential Equations
We consider a normal autonomous system of differential equations with a small parameter, which has a critical linear approximation at zero value of...
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Non-autonomous Differential Systems with Delays: A Global Attraction Analysis
In this paper, we derive criteria of global attractivity of a (possibly constant) positive periodic solution in non-autonomous systems of delay...
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Well-posedness of non-autonomous transport equation on metric graphs
We consider transport processes on metric graphs with time-dependent velocities and show that, under continuity assumption of the velocity...
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Existence and optimal controls of non-autonomous for impulsive evolution equation without Lipschitz assumption
In this paper, we investigate the existence of mild solutions as well as optimal controls for non-autonomous impulsive evolution equations with...
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A Higher-Order Non-autonomous Semilinear Parabolic Equation
In this paper, we study results of well-posedness and regularity of higher order in time abstract non-autonomous semilinear Cauchy problems...
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On the Preservation of a Quadratic Lyapunov Function of a Linear Differential Autonomous System under Constant Perturbations of the Coefficients
AbstractFor an autonomous linear homogeneous asymptotically stable differential system, we obtain sufficient conditions for the smallness of...
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Existence of Local and Maximal Mild Solutions for Some Non-autonomous Functional Differential Equation with Finite Delay
This chapter is devoted to the study of the existence results of local and maximal solutions on the one hand and the existence and uniqueness results...
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A note on blow-up solutions for a scalar differential equation with a discrete delay
We study blow-up solutions for a general scalar differential equation with a discrete delay. It is shown that the existence of blow-up solutions for...
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Approximate Controllability for Mixed Type Non-autonomous Fractional Differential Equations
In this paper, we discuss the approximate controllability for mixed type non-autonomous fractional differential equations. By using the Schauder...
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Adomian’s Decomposition Method in the Theory of Nonlinear Autonomous Boundary-Value Problems
For a nonlinear autonomous boundary-value problem posed for an ordinary differential equation in the critical case, we establish constructive...
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On a Nonlinear Second-Order Ordinary Differential Equation
AbstractWe consider a nonlinear second-order ordinary differential equation of a special form whose particular case arises when constructing exact...