Related papers: Tikhonov Theorem for Differential Equations with S…
Sturm oscillation theorem for second order differential equations was generalized to systems and higher order equations with positive leading coefficient by several authors. What we propose here is a Sturm oscillation theorem for systems of…
Stability of stationary solutions of parabolic equations is conventionally studied by linear stability analysis, Lyapunov functions or lower and upper functions. We discuss here another approach based on differential inequalities written…
Second order linear non-autonomous differential equations with negative stiffness are considered. Using Chetaev-like (Lyapunov-like) functions, necessary (sufficient) conditions are found for the solutions to be bounded for all initial…
This paper is concerned with stability analysis of nonlinear time-varying systems by using Lyapunov function based approach. The classical Lyapunov stability theorems are generalized in the sense that the time-derivative of the Lyapunov…
Sturm theory for second order differential equations was generalized to systems and higher order equations with positive leading coefficient by several authors. Here we propose a Sturm oscillation theorem for indefinite systems of even…
A new approximation of the discriminant of a second order periodic differential equation is presented as a recursive summation of the evaluation of its excitation function at different values of time. The new approximation is obtained, at…
We consider a continuous-time linear time-invariant dynamical system that admits an invariant cone. For the case of a self-dual and homogeneous cone we show that if the system is asymptotically stable then it admits a quadratic Lyapunov…
The article summarizes some developments about a singular versions of the Sturm Comparison and Separation theorems where the coefficients or the interval of definition may be unbounded.
We prove Marchenko-type uniqueness theorems for inverse Sturm-Liouville problems. Moreover, we prove a generalization of Ambarzumyans theorem.
Looped-functionals have been shown to be relevant for the analysis of a wide variety of systems. However, the conditions obtained in previous works on the analysis of sampled-data, impulsive and switched systems have only been shown to be…
This paper introduces a modeling framework that is suitable to resolve singularities of impact phenomena encountered in applications. The method involves an exact transformation that turns the continuum, often partial differential equation…
Lyapunov functions with exponential weights have been used successfully as a powerful tool for the stability analysis of hyperbolic systems of balance laws. In this paper we extend the class of weight functions to a family of hyperbolic…
We apply a Lyapunov function to obtain conditions for the existence and uniqueness of small classical time-periodic solutions to first order quasilinear 1D hyperbolic systems with (nonlinear) nonlocal boundary conditions in a strip. The…
The main objective of this paper is the construction of the solution of an impulsive stochastic differential equation, subject to control conditions in the pulse-times and give sufficient conditions for them to be random variables with…
We consider Fredholm integral equation of the first kind, present an efficient new iterated Tikhonov method to solve it. The new Tikhonov iteration method has been proved which can achieve the optimal order under a-priori assumption. In…
We consider a degenerate stochastic differential equation that has a sticky point in the Markov process sense. We prove that weak existence and weak uniqueness hold, but that pathwise uniqueness does not hold nor does a strong solution…
Discrete differential equations appear most prominently in planar map and lattice path enumeration. In this work we consider discrete differential equations with an additional parameter $x$, where the order of the equation is $1$ for $x=0$…
We find some new results regarding the existence, uniqueness, boundedness, stability and attractivity of the solutions of a class of initial-boundary-value problems characterized by a quasi-linear third order equation which may have…
The distributional properties of a multi-dimensional continuous-state branching process are determined by its cumulant semigroup, which is defined by the backward differential equation. We provide a proof of the assertion of Rhyzhov and…
The fundamental matrix and the delay Lyapunov matrix of linear delay difference equations are introduced. Some properties of the Lyapunov matrix, and the jump discontinuities of its derivative are proven, leading to its construction in the…