Reduction principle in the theory of stability of difference equations
Andrejs Reinfelds Klara Janglajew
Conference Publications 2007, 2007(Special): 864-874 doi: 10.3934/proc.2007.2007.864
The reduction principle is generalized to the case of the nonautonomous difference equations in Banach space whose right-handed side is allowed to be noninvertible and whose linear part satisfies weaker condition than exponential dichotomy.
keywords: asymptotic phase. stability of solutions invariant manifold Reduction principle
An explicit coefficient criterion for the existence of positive solutions to the linear advanced equation
Josef Diblík Klara Janglajew Mária Kúdelčíková
Discrete & Continuous Dynamical Systems - B 2014, 19(8): 2461-2467 doi: 10.3934/dcdsb.2014.19.2461
The paper is devoted to the investigation of a linear differential equation with advanced argument $\dot y(t)=c(t)y(t+\tau),$ where $\tau>0$, and the function $c\colon [t_0,\infty)\to (0,\infty)$, $t_0\in \mathbb{R}$ is bounded and locally Lipschitz continuous. New explicit coefficient criterion for the existence of a positive solution in terms of $c$ and $\tau$ is derived.
keywords: positive solution implicit criterion explicit criterion Advanced linear differential equation asymptotic expansion.

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