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The oscillation of higher-order differential equations with deviating arguments

โœ Scribed by R.P. Agarwal; S.R. Grace

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
713 KB
Volume
38
Category
Article
ISSN
0898-1221

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โœฆ Synopsis

In this paper, some new criteria for the oscillation of higher-order functional differential equations of the form Lnx(t) + F (t, x(g(t))) = O, n is even are established. Some of our results are obtained via comparing it with second-order ordinary linear and first-order delay differential equations. The oscillation of this equation when n is odd is also considered. Then, we shall use the obtained results to study the oscillatory behavior of the neutral functional differential equations of the form

Ln (x(t) + c(t)z(v(t))) + F(t, x(g(t))) = O, n is even

and the damped functional differential equations of the type Lnx(t)+H (t,x(g(t)),dx(h(t))) =0, n is even.

The obtained results extend, improve, and correlate a number of existing criteria. (~) 1999 Elsevier Science Ltd. All rights reserved.

๐Ÿ“œ SIMILAR VOLUMES

Oscillation of even order partial differ
Oscillation of even order partial differential equations with distributed deviating arguments
โœ Gaihua Gui; Zhiting Xu ๐Ÿ“‚ Article ๐Ÿ“… 2009 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 586 KB

Some Kamenev-type oscillation criteria are established for a class of boundary value problems associated with even-order partial differential equations with distributed deviating arguments. Our approach is to reduce the high-dimensional oscillation problem to a one-dimensional oscillation one, and t