Oscillation Results for Higher Order Differential Equations
نویسندگان
چکیده
منابع مشابه
Oscillation Theorems for Certain Higher Order Nonlinear Functional Differential Equations
Some new oscillation theorems for higher-order nonlinear functional differential equations of the form d n dt n a(t) d n x(t) dt n α + q(t)f x g(t) = 0, α > 0, are established.
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We establish some oscillation criteria for the solutions to forced higher-order differential equations. We do not assume that the forcing term is the n-th derivative of an oscillatory function, and do not assume that the coefficients are of a definite sign. Our results are illustrated with examples.
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Hence, q is bounded from above and limt→∞ q(t) = q∞ <∞. Note that the function r may change sign. By a solution of () we mean a function x differentiable up to order n which satisfies () on [Tx,∞), Tx ≥ . A solution of () is said to be proper if sup{|x(t)| : t ≥ T} > for any T ≥ Tx. As usual, a solution x of () is said to be oscillatory if x changes sign for large t. The aim of this pape...
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In this article, we use the Riccati transformation technique and some inequalities, to establish oscillation theorems for all solutions to evenorder quasilinear neutral differential equation “ˆ` x(t) + p(t)x(τ(t)) ́(n−1) ̃γ”′ + q(t)x ` σ(t) ́ = 0, t ≥ t0. Our main results are illustrated with examples.
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Some new criteria have been established for the oscillation of higher-order forced nonlinear differential equation of the form Lnx(t) + q(t)F(x(t)) = e(t) according to the smart choice of a class of new auxiliary functions. No restriction is imposed on the forcing term e(t) as those assumed in [A.G. Kartsatos, Maintenance of oscillations under the effect of a periodic forcing term, Proc. Amer. ...
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ژورنال
عنوان ژورنال: Axioms
سال: 2020
ISSN: 2075-1680
DOI: 10.3390/axioms9010014