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Zbl 1056.34063
Berezansky, Leonid; Domshlak, Yury; Braverman, Elena
On oscillation properties of delay differential equations with positive and negative coefficients. (English)
[J] J. Math. Anal. Appl. 274, No. 1, 81-101 (2002). ISSN 0022-247X

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 2000:: *34K11 Oscillation theory of functional-differential equations
34K12 Properties of solutions of functional-differential equations

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