Related papers: Asymptotic condition numbers for linear ordinary d…
This paper introduces, up to the author's knowledge, for the first time the generalized initial value problem. In this problem, given an ordinary differential equation defined in some set, the initial conditions are mapped to a subset of…
We consider perturbations of nonlinear eigenvalue problems driven by a nonhomogeneous differential operator plus an indefinite potential. We consider both sublinear and superlinear perturbations and we determine how the set of positive…
This paper establishes the precise asymptotic behavior, as time $t$ tends to infinity, for nontrivial, decaying solutions of genuinely nonlinear systems of ordinary differential equations. The lowest order term in these systems, when the…
Consider the first-order linear differential equation with several retarded arguments $$ x^{\prime}(t)+\sum\limits_{i=1}^{m}p_{i}(t)x(\tau_{i}(t))=0,\;\;\;t\geq t_{0}, $$ where the functions $p_{i},\tau_{i}\in…
We study evolution equations governed by an averaging operator on a directed tree, showing existence and uniqueness of solutions. In addition we find conditions of the initial condition that allows us to find the asymptotic decay rate of…
Various types of stabilizing controls lead to a deterministic difference equation with the following property: once the initial value is positive, the solution tends to the unique positive equilibrium. Introducing additive perturbations can…
The dynamics of the second order rational difference equation in the title with complex parameters and arbitrary complex initial conditions is investigated. Two associated difference equations are also studied. The solutions in the complex…
Linear scalar differential equations with distributed delays appear in the study of the local stability of nonlinear differential equations with feedback, which are common in biology and physics. Negative feedback loops tend to promote…
Derivatives of fractional order are introduced in different ways: as left-inverse of the fractional integral or by generalizing the limit of the difference quotient defining integer-order derivatives. Although the two approaches lead (under…
Many numerical problems with input $x$ and output $y$ can be formulated as a system of equations $F(x, y) = 0$ where the goal is to solve for $y$. The condition number measures the change of $y$ for small perturbations to $x$. From this…
The long time effect of nonlinear perturbation to oscillatory linear systems can be characterized by the averaging method, and we consider first-order averaging for its simplest applicability to high-dimensional problems. Instead of the…
In this article, the order of some classes of fractional linear differential equations is determined, based on asymptotic behavior of the solution as time tends to infinity. The order of fractional derivative has been proved to be of great…
The theme of this article is to provide some sufficient conditions for the asymptotic property and oscillation of all solutions of third-order half-linear differential equations with advanced argument of the form…
We suggest a modification of the operator exponential method for the numerical solving the difference linear initial boundary value problems. The scheme is based on the representation of the difference operator for given boundary conditions…
In this paper, we consider one--parameter ($\lambda>0$) families of Li\'enard differential equations. We are concerned with the study on the asymptotic behavior of periodic solutions for small and large values of $\lambda>0$. To prove our…
We consider the asymptotic solutions of an interface problem corresponding to an elliptic partial differential equation with Dirich- let boundary condition and transmission condition, subject to the small geometric perturbation and the high…
In the literature on singular perturbation (Lavrentiev regularization) for the stable approximate solution of operator equations with monotone operators in the Hilbert space the phenomena of conditional stability and local well-posedness…
Exponential stability and solution estimates are investigated for a delay system $$ \dot{x}(t) - A(t)\dot{x}(g(t))=\sum_{k=1}^m B_k(t)x(h_k(t)) $$ of a neutral type, where $A$ and $B_k$ are $n\times n$ bounded matrix functions, and $g, h_k$…
In this paper, we study both the oscillation and the stability of impulsive differential equations when not only the continuous argument but also the impulse condition involves delay. The results obtained in the present paper improve and…
The condition number of the $n\ x\ n$ matrix $P$ is examined, where $P$ solves %the discete Lyapunov equation, $P - A P A^* = BB^*$, and $B$ is a $n\ x\ d$ matrix. Lower bounds on the condition number, $\kappa$, of $P$ are given when $A$ is…