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

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• 作者：Josef Diblí ; k ^{josef.diblik@ceitec.vutbr.cz" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Positive solution ; Advanced-argument ; Integral criterion
• 刊名：Applied Mathematics Letters
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：63
• 期：Complete
• 页码：40-45
• 全文大小：561 K

文摘

A linear differential equation with advanced-argument y^′(t)−c(t)y(t+τ)=0$y^{\prime }\left(t\right)-c\left(t\right)y(t+\tau )=0$ is considered where c:[t₀,∞)→[0,∞)$c:[t_0,\infty )\to [0,\infty )$, t₀∈R$t_0\in \mathbb{R}$ is a bounded and locally Lipschitz continuous function and τ>0$\tau >0$. The well-known explicit integral criterion guarantees the existence of a positive solution on [t₀,∞)$[t_0,\infty )$. The paper derives new integral criteria involving the coefficient c$c$. Their independence of the previous result is discussed as well.