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 class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0893965916302105&_mathId=si1.gif&_user=111111111&_pii=S0893965916302105&_rdoc=1&_issn=08939659&md5=2da34cee5eb6e94bcfa9ce823af575b0" title="Click to view the MathML source">y^′(t)−c(t)y(t+τ)=0class="mathContainer hidden">class="mathCode">$y^{\prime }\left(t\right)-c\left(t\right)y(t+\tau )=0$ is considered where class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0893965916302105&_mathId=si2.gif&_user=111111111&_pii=S0893965916302105&_rdoc=1&_issn=08939659&md5=af020a8cf678369fa52c10c9cdbd9af6" title="Click to view the MathML source">c:[t₀,∞)→[0,∞)class="mathContainer hidden">class="mathCode">$c:[t_0,\infty )\to [0,\infty )$, class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0893965916302105&_mathId=si3.gif&_user=111111111&_pii=S0893965916302105&_rdoc=1&_issn=08939659&md5=6cf95e87662230b218c82538146efa5e" title="Click to view the MathML source">t₀∈Rclass="mathContainer hidden">class="mathCode">$t_0\in \mathbb{R}$ is a bounded and locally Lipschitz continuous function and class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0893965916302105&_mathId=si4.gif&_user=111111111&_pii=S0893965916302105&_rdoc=1&_issn=08939659&md5=37ee10d669c6b442c19f8f40ad635c40" title="Click to view the MathML source">τ>0class="mathContainer hidden">class="mathCode">$\tau >0$. The well-known explicit integral criterion guarantees the existence of a positive solution on class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0893965916302105&_mathId=si6.gif&_user=111111111&_pii=S0893965916302105&_rdoc=1&_issn=08939659&md5=5043ae5d3d6911c31d8396be43db67c4" title="Click to view the MathML source">[t₀,∞)class="mathContainer hidden">class="mathCode">$[t_0,\infty )$. The paper derives new integral criteria involving the coefficient class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0893965916302105&_mathId=si7.gif&_user=111111111&_pii=S0893965916302105&_rdoc=1&_issn=08939659&md5=4b880d4f772fd6d56ae634b35aa04608" title="Click to view the MathML source">cclass="mathContainer hidden">class="mathCode">$c$. Their independence of the previous result is discussed as well.