A linear differential equation with advanced-argument   y ′ (t)−c(t)y(t+τ)=0       y    ′     (  t  )   −  c   (  t  )   y   (  t  +  τ  )   =  0        is considered where   c:[t 0 ,∞)→[0,∞)     c  :   [    t    0    ,  ∞  )   →   [  0  ,  ∞  )        ,   t 0 ∈R       t    0    ∈  R        is a bounded and locally Lipschitz continuous function and   τ>0     τ  >  0       . The well-known explicit integral criterion                ∫    t    t  +  τ    c   (  s  )        d   s  ≤  1  /   e   ,    t  ∈   [    t    0    ,  ∞  )             guarantees the existence of a positive solution on   [t 0 ,∞)      [    t    0    ,  ∞  )        . The paper derives new integral criteria involving the coefficient   c     c       . Their independence of the previous result is discussed as well.
['Josef Diblík']
Integral criteria for the existence of positive solutions of first-order linear differential advanced-argument equations