Integral criteria for the existence of positive solutions of first-order linear differential advanced-argument equations

Integral criteria for the existence of positive solutions of first-order linear differential advanced-argument equations

WoS Article

A linear differential equation with advanced-argument $y'(t)-c(t)y(t+\tau)=0$ is considered where $c\colon [t_0,\infty)\to [0,\infty)$, $t_0\in \bR$ is a bounded and locally Lipschitz continuous function and $\tau>0$. The well-known explicit integral criterion $$ \int_{t}^{t+\tau}c(s)\,\diff s\le{1}/{\e}\,,\,\,\,t\in[t_0,\infty) $$ guarantees the existence of a positive solution on $[t_0,\infty)$. The paper derives new integral criteria involving the coefficient $c$. Their independence of the previous result is discussed as well.

A linear differential equation with advanced-argument $y'(t)-c(t)y(t+\tau)=0$ is considered where $c\colon [t_0,\infty)\to [0,\infty)$, $t_0\in \bR$ is a bounded and locally Lipschitz continuous function and $\tau>0$. The well-known explicit integral criterion $$ \int_{t}^{t+\tau}c(s)\,\diff s\le{1}/{\e}\,,\,\,\,t\in[t_0,\infty) $$ guarantees the existence of a positive solution on $[t_0,\infty)$. The paper derives new integral criteria involving the coefficient $c$. Their independence of the previous result is discussed as well.

Positive solution, advanced-argument, integral criterion.

Positive solution, advanced-argument, integral criterion.

DIBLÍK, J.

2018

31.01.2017

Elsevier

0893-9659

Applied Mathematics Letters

72

10

United States of America

40

45

8

https://doi.org/10.1016/j.aml.2016.07.016