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"> 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">,
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"> 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">. The well-known explicit integral criterion
class="formula" id="fd000005">
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">. 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">. Their independence of
the previous result is discussed as well.