Exact Conditions of Oscillation of Solutions to Differential Equations with Several Delays
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We obtain new nonimprovable conditions of oscillation of all solutions to a linear differential equation with several variable delays and positive coefficients. These conditions have the form of the upper and lower limits of the sum of integrals of the coefficients over the sets that are determined only by the delay corresponding to this coefficient. These results differ from the well-known results in which a coarsening of the integration set is assumed.
Keywords and phrasesdifferential equation with several delays oscillation effective condition
AMS Subject Classification34K06 34K11
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- 9.G. Ladas, V. Lakshmikantham, and J. S. Papadakis, “Oscillations of higher-order retarded differential equations generated by the retarded argument,” in: Proc. Conf. “Delay and Functional Differential Equations and Their Applications, Park City, Utah, 1972, Academic Press, New York (1972), pp. 219–231.Google Scholar