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On oscillation properties of delay differential equations with positive and negative coefficients. (English) Zbl 1056.34063
J. Math. Anal. Appl. 274, No. 1, 81-101 (2002); corrigendum ibid. 351, No. 2, 819-820 (2009).
Summary: For a scalar delay differential equation
$x^{\prime}(t) +a(t)x(h(t))-b(t)x(g(t))=0,\quad t\geq t_{0},\tag{E}$
where $$a(t)\geq 0$$, $$b(t)\geq 0$$, $$h(t)\leq t$$, $$g(t)\leq t$$, a connection between the following properties is established: nonoscillation of the differential equation and the corresponding differential inequalities, positiveness of the fundamental function and existence of a nonnegative solution for a certain explicitly constructed nonlinear integral inequality. A comparison theorem and explicit nonoscillation and oscillation results are presented.

##### MSC:
 34K11 Oscillation theory of functional-differential equations 34K12 Growth, boundedness, comparison of solutions to functional-differential equations
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##### References:
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