On oscillation properties of delay differential equations with positive and negative coefficients
نویسندگان
چکیده
For a scalar delay differential equation ẋ(t)+ a(t)x(h(t))− b(t)x(g(t))= 0, a(t) 0, b(t) 0, h(t) t, g(t) 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. 2002 Elsevier Science (USA). All rights reserved. * Corresponding author. E-mail addresses: [email protected] (L. Berezansky), [email protected], [email protected] (E. Braverman). 1 Now on leave in Yale University, Department of Mathematics, 10 Hillhouse Avenue, PO Box 208283, New Haven, CT 06520-8283, USA. 0022-247X/02/$ – see front matter 2002 Elsevier Science (USA). All rights reserved. PII: S0022-247X(02)00 24 69 82 L. Berezansky et al. / J. Math. Anal. Appl. 274 (2002) 81–101
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