Displaying similar documents to “Integral averaging techniques for oscillation of second order nonlinear differential equations with damping.”

Oscillation results for second order nonlinear differential equations

Jozef Džurina, Dáša Lacková (2004)

Open Mathematics

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In this paper, the authors present some new results for the oscillation of the second order nonlinear neutral differential equations of the form r t ψ x t x t + p t x τ t ' ' + q t f x σ t = 0 . Easily verifiable criteria are obtained that are also new for differential equations without neutral term i.e. for p(t)≡0.

Oscillation theorems for certain even order neutral differential equations

Qi Gui Yang, Sui-Sun Cheng (2007)

Archivum Mathematicum

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This paper is concerned with a class of even order nonlinear differential equations of the form d d t | x ( t ) + p ( t ) x ( τ ( t ) ) ( n - 1 ) | α - 1 ( x ( t ) + p ( t ) x ( τ ( t ) ) ) ( n - 1 ) + F ( t , x ( g ( t ) ) ) = 0 , where n is even and t ≥ t 0 . By using the generalized Riccati transformation and the averaging technique, new oscillation criteria are obtained which are either extensions of or complementary to a number of existing results. Our results are more general and sharper than some previous results even for second order equations.