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Oscillation Criteria For Delay Equations
, 2000
"... . This paper is concerned with the oscillatory behavior of firstorder delay differential equations of the form x 0 (t) + p(t)x((t)) = 0; t t 0 ; (1) where p; 2 C([t 0 ; 1);R + ); R + = [0; 1); (t) is nondecreasing, (t) ! t for t t 0 and lim t!1 (t) = 1. Let the numbers k and L be define ..."
Abstract

Cited by 7 (1 self)
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. This paper is concerned with the oscillatory behavior of firstorder delay differential equations of the form x 0 (t) + p(t)x((t)) = 0; t t 0 ; (1) where p; 2 C([t 0 ; 1);R + ); R + = [0; 1); (t) is nondecreasing, (t) ! t for t t 0 and lim t!1 (t) = 1. Let the numbers k and L be defined by k = lim inf t!1 Z t (t) p(s)ds and L = lim sup t!1 Z t (t) p(s)ds: It is proved here that when L ! 1 and 0 ! k 1 e all solutions of Eq. (1) oscillate in several cases in which the condition L ? 2k + 2 1 \Gamma 1 holds, where 1 is the smaller root of the equation = e k . 1. Introduction The problem of establishing sufficient conditions for the oscillation of all solutions of the differential equation x 0 (t) + p(t)x( (t)) = 0; t t 0 ; (1) where the functions p; 2 C([t 0 ; 1); R + ) (here R + = [0; 1)); (t) is nondecreasing, (t) ! t for t t 0 and lim t!1 (t) = 1, has been the subject of many investigations. See, for example, [1][26] and the references ci...
Oscillation Of Volterra Integral Equations And Forced Functional Differential Equations
, 1993
"... this paper [19, 20]. ..."