相关论文: On the Asymptotic Integration of a System of Linea…

In this paper, we study the asymptotic behavior of solutions to a scalar fractional delay differential equations around the equilibrium points. More precise, we provide conditions on the coefficients under which a linear fractional delay…

In this paper we study the asymptotic behavior of nonoscillatory solutions for high order differential equations of Poincar\'e type. We introduce two new and more weak than classical hypotheses on the coefficients, which implies a well…

Let $\Omega \subset \mathbb{R}^n$ be a bounded smooth domain (open and connected) in $\mathbb{R}^n$. Given $u_0\in L^2(\Omega)$, $g\in L^\infty(\Omega)$ and $\lambda \in \mathbb{R}$, our purpose is to describe the asymptotic behavior of…

Time-decaying perturbations of nonlinear oscillatory systems in the plane are considered. It is assumed that the unperturbed systems are non-isochronous and the perturbations oscillate with an asymptotically constant frequency. Resonance…

We consider an abstract linear wave equation with a time-dependent dissipation that decays at infinity with the so-called scale invariant rate, which represents the critical case. We do not assume that the coefficient of the dissipation…

In this paper, we consider the asymptotic stability for a system of linear delay differential equations. By analysing of the characteristic equation in detail, we have established the necessary and sufficient condition for the asymptotic…

We prove the theorem of linearized asymptotic stability for fractional differential equations. More precisely, we show that an equilibrium of a nonlinear Caputo fractional differential equation is asymptotically stable if its linearization…

We give an exact result about the asymptotic limit of an oscillatory integral whose phase contains a certain flat term. Corresponding to the real analytic phase case, one can see an essential difference in the behavior of the above…

The asymptotic iteration method (AIM) is an iterative technique used to find exact and approximate solutions to second-order linear differential equations. In this work, we employed AIM to solve systems of two first-order linear…

As to methods for expanding an oscillatory integral into an asymptotic series with respect to the parameter, the method of stationary phase for the non-degenerate phases and the method of using resolution of singularities for degenerate…

We estimate the growth in time of the solutions to a class of nonlinear fractional differential equations $D_{0+}^{\alpha}(x-x_0) =f(t,x)$ which includes $D_{0+}^{\alpha}(x-x_0) =H(t)x^{\lambda}$ with $\lambda\in(0,1)$ for the case of…

Time-decaying harmonic oscillators yield dispersive estimates with weak decay, and change the threshold power of the nonlinearity between the short and the long range. In the non-critical case for the time-decaying harmonic oscillator, this…

Consider an integral $I(s):=\int_0^T e^{-s(x^2-icx)}dx$, where $c>0$ and $T>0$ are arbitrary positive constants. It is proved that $I(s)\sim \frac{i}{sc}$ as $s\to +\infty$. The asymptotic behavior of the integral…

In this work we study the asymptotic behavior of solutions for a general linear second-order evolution differential equation in time with fractional Laplace operators in $\mathbb{R}^n$. We obtain improved decay estimates with less demand on…

The asymptotic behavior, as $T\to\infty$, of some functionals of the form $I_T(t)=F_T(\xi_T(t))+\int_0^tg_T(\xi_T(s))\,dW_T(s)$, $t\ge0$ is studied. Here $\xi_T(t)$ is the solution to the time-inhomogeneous It\^{o} stochastic differential…

Classical conditions for asymptotic stability of periodic solutions bifurcating from a limit cycle rely on the derivative of the corresponding bifurcation function F at the bifurcation point t. We show that for analytic systems this result…

This paper studies the dynamics of families of monotone nonautonomous neutral functional differential equations with nonautonomous operator, of great importance for their applications to the study of the long-term behavior of the…

A pair of linearly independent asymptotic solutions are constructed for the second-order linear difference equation {equation*} P_{n+1}(x)-(A_{n}x+B_{n})P_{n}(x)+P_{n-1}(x)=0, {equation*} where $A_n$ and $B_n$ have asymptotic expansions of…

We analyze a simple example of wave equation with a time-dependent damping term, whose coefficient decays at infinity at the scale-invariant rate and includes an oscillatory component that is integrable but not absolutely integrable. We…

We present a hybrid study that combines a concise review of scalar-field cosmology with new analytic developments that integrate averaging reductions for oscillatory regimes with dynamical-systems techniques. For oscillatory fields, we…