Correct Solvability of Nonlinear Ordinary Differential Equations in Orlicz Spaces

Hyperbolicity and solvability for linear systems on time scales

We believe that the difference between time scale systems and ordinary differential equations is not as big as people use to think. We consider linear operators that correspond to linear dynamic systems on time scales. We study solvability of these operators in ${\mathbb L}^\infty$. For ordinary differential equations such solvability is equivalent to hyperbolicity of the considered linear system. Using this approach and transformations of the time variable, we spread the concept of hyperbolicity to time scale dynamics. We provide some analogs of well-known facts of Hyperbolic Systems Theory, …

时间尺度上几乎线性动力系统的有界解与指数衰减解

Bounded and exponentially decaying solutions of almost linear dynamic systems on time scales

本文研究时间尺度上线性系统的小非线性扰动，通过Δ-微分算子在函数空间中的可解性方法，推广了指数二分性并引入Lyapunov正则性条件，证明了扰动系统有界解的存在性判据。

Nonoscillation and Stability of the Second Order Ordinary Differential Equations with a Damping Term

In this paper we consider the linear ordinary equation of the second order $$ L x(t)\equiv \ddot{x}(t) +a(t)\dot{x}(t)+b(t)x(t)=f(t), \eqno{(1)} $$ and the corresponding homogeneous equation $$ \ddot{x}(t) +a(t)\dot{x}(t)+b(t)x(t)=0. \eqno{(2)} $$ Note that $[α,β]$ is called a nonoscillation interval if every nontrivial solution has at most one zero on this interval. Many investigations which seem to have no connection such as differential inequalities, the Polia-Mammana decomposition (i.e. representation of the operator $L$ in the form of products of the first order differential operators), u…

最简单大时滞微分方程的多尺度分析

Multiple-scale analysis of the simplest large-delay differential equation

本研究针对大时滞微分方程与空间扩展动力系统的关联问题，通过多尺度分析最简单的线性DDE，证明其与扩散方程的渐近对应，揭示了大时滞极限下首阶映射及久期发散的来源，深化了DDE的理论认知。