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Oscillation Criteria of Comparison Type for Nonlinear Functional Differential Equations

✍ Scribed by S. R. Grace

Publisher
John Wiley and Sons
Year
1995
Tongue
English
Weight
642 KB
Volume
173
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

In this paper we relate the oscillation problem of the nonlinear functional differential equation (a(t)x'(t))' + q(t) f (x(g(t)))= 0 and the nonlinear neutral functional differential equation (a(t) (x(t)+ p(t)x(g^*^(t)))'} + q(t)f (x(g(t))) = 0 to some linear second order ordinary differential equations. Recent results on linear oscillation can thus be used to obtain interesting oscillation criteria for the nonlinear equations. Similar results for the forced nonlinear functional differential equation (a(t)x'(t))' + q(t) f (x(g(t)))= e(t) and the forced neutral functional differential equation (a(t) (x(t)+ mx(t β€” n))')' + q(t) f (x(g(t)))= e(t) are also established. The function f appeared in the above equations is not require to be monotone.

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