Displaying similar documents to “On oscillatory nonlinear fourth-order difference equations with delays”

On the oscillation of solutions of third order linear difference equations of neutral type

Anna Andruch-Sobiło, Małgorzata Migda (2005)

Mathematica Bohemica

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In this note we consider the third order linear difference equations of neutral type Δ 3 [ x ( n ) - p ( n ) x ( σ ( n ) ) ] + δ q ( n ) x ( τ ( n ) ) = 0 , n N ( n 0 ) , ( E ) where δ = ± 1 , p , q N ( n 0 ) + ; σ , τ N ( n 0 ) , lim n σ ( n ) = lim n τ ( n ) = . We examine the following two cases: { 0 < p ( n ) 1 , σ ( n ) = n + k , τ ( n ) = n + l } , { p ( n ) > 1 , σ ( n ) = n - k , τ ( n ) = n - l } , where k , l are positive integers and we obtain sufficient conditions under which all solutions of the above equations are oscillatory.

Bounded oscillation of nonlinear neutral differential equations of arbitrary order

Yeter Ş. Yilmaz, Ağacik Zafer (2001)

Czechoslovak Mathematical Journal

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The paper is concerned with oscillation properties of n -th order neutral differential equations of the form [ x ( t ) + c x ( τ ( t ) ) ] ( n ) + q ( t ) f x ( σ ( t ) ) = 0 , t t 0 > 0 , where c is a real number with | c | 1 , q C ( [ t 0 , ) , ) , f C ( , ) , τ , σ C ( [ t 0 , ) , + ) with τ ( t ) < t and lim t τ ( t ) = lim t σ ( t ) = . Sufficient conditions are established for the existence of positive solutions and for oscillation of bounded solutions of the above equation. Combination of these conditions provides necessary and sufficient conditions for oscillation of bounded solutions of the equation. Furthermore, the results are generalized to equations...

Oscillations of certain functional differential equations

Said R. Grace (1999)

Czechoslovak Mathematical Journal

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Sufficient conditions are presented for all bounded solutions of the linear system of delay differential equations ( - 1 ) m + 1 d m y i ( t ) d t m + j = 1 n q i j y j ( t - h j j ) = 0 , m 1 , i = 1 , 2 , ... , n , to be oscillatory, where q i j ε ( - , ) , h j j ( 0 , ) , i , j = 1 , 2 , ... , n . Also, we study the oscillatory behavior of all bounded solutions of the linear system of neutral differential equations ( - 1 ) m + 1 d m d t m ( y i ( t ) + c y i ( t - g ) ) + j = 1 n q i j y j ( t - h ) = 0 , where c , g and h are real constants and i = 1 , 2 , ... , n .

Oscillatory properties of third-order semi-noncanonical nonlinear delay difference equations

Govindasamy Ayyappan, George E. Chatzarakis, Thaniarasu Kumar, Ethiraj Thandapani (2023)

Mathematica Bohemica

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We study the oscillatory properties of the solutions of the third-order nonlinear semi-noncanonical delay difference equation D 3 y ( n ) + f ( n ) y β ( σ ( n ) ) = 0 , where D 3 y ( n ) = Δ ( b ( n ) Δ ( a ( n ) ( Δ y ( n ) ) α ) ) is studied. The main idea is to transform the semi-noncanonical operator into canonical form. Then we obtain new oscillation theorems for the studied equation. Examples are provided to illustrate the importance of the main results.

Oscillation theorems for third order nonlinear delay difference equations

Kumar S. Vidhyaa, Chinnappa Dharuman, Ethiraju Thandapani, Sandra Pinelas (2019)

Mathematica Bohemica

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Sufficient conditions are obtained for the third order nonlinear delay difference equation of the form Δ ( a n ( Δ ( b n ( Δ y n ) α ) ) ) + q n f ( y σ ( n ) ) = 0 to have property ( A ) or to be oscillatory. These conditions improve and complement many known results reported in the literature. Examples are provided to illustrate the importance of the main results.

Existence of nonoscillatory solutions to third order neutral type difference equations with delay and advanced arguments

Srinivasan Selvarangam, Sethurajan A. Rupadevi, Ethiraju Thandapani, Sandra Pinelas (2021)

Mathematica Bohemica

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In this paper, we present several sufficient conditions for the existence of nonoscillatory solutions to the following third order neutral type difference equation Δ 3 ( x n + a n x n - l + b n x n + m ) + p n x n - k - q n x n + r = 0 , n n 0 via Banach contraction principle. Examples are provided to illustrate the main results. The results obtained in this paper extend and complement some of the existing results.