Oscillation criteria for delay equations

This paper is concerned with the oscillatory behavior of first-order delay differential equations of the form (1) x'(t) + p(t)x(tau(t)) = 0, t greater than or equal to t(0), where p, tau is an element of C([t(0), infinity), R+), R+ = [0, infinity), tau(t) is non-decreasing, tau(t) < t for t greater than or equal to t(0) an d lim(t-->infinity) tau(t) = infinity. Let the numbers k and L be defined b y [GRAPHICS] It is proved here that when L < 1 and 0 < k less than or equal to 1/e all s olutions of Eq. (1) oscillate in several cases in which the condition L > 2k + 2/lambda(1) -1 holds, where lambda(1) is the smaller root of the equation lambda = e(k lam bda).