PROC
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
DCDS-B
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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