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On the oscillation of certain third-order difference equations.

Agarwal, Ravi P.; Grace, Said R.; O'Regan, Donal — 2005

Advances in Difference Equations [electronic only]

Oscillation criteria for first-order forced nonlinear difference equations.

Agarwal, Ravi P.; Grace, Said R.; Smith, Tim — 2006

Advances in Difference Equations [electronic only]

Linearization and higher order nonlinear oscillation theorems using comparison methods.

Agarwal, Ravi P.; Grace, Said R.; O'Regan, Donal — 2004

Georgian Mathematical Journal

Oscillation of certain difference equations

Said R. Grace — 2000

Czechoslovak Mathematical Journal

Some new criteria for the oscillation of difference equations of the form $Δ^{2} x_{n} - p_{n} Δ x_{n - h} + q_{n} {| x_{g_{n}} |}^{c} s g n x_{g_{n}} = 0$ and $Δ^{i} x_{n} + p_{n} Δ^{i - 1} x_{n - h} + q_{n} {| x_{g_{n}} |}^{c} s g n x_{g_{n}} = 0, i = 2, 3,$ are established.

Oscillations of certain functional differential equations

Said R. Grace — 1999

Czechoslovak Mathematical Journal

Sufficient conditions are presented for all bounded solutions of the linear system of delay differential equations ${(- 1)}^{m + 1} \frac{d^{m} y_{i} (t)}{d t^{m}} + \sum_{j = 1}^{n} q_{i j} y_{j} (t - h_{j j}) = 0, m \geq 1, i = 1, 2, ..., n,$ to be oscillatory, where $q_{i j} ε (- \infty, \infty)$ , $h_{j j} \in (0, \infty)$ , $i, j = 1, 2, ..., n$ . Also, we study the oscillatory behavior of all bounded solutions of the linear system of neutral differential equations ${(- 1)}^{m + 1} \frac{d^{m}}{d t^{m}} (y_{i} (t) + c y_{i} (t - g)) + \sum_{j = 1}^{n} q_{i j} y_{j} (t - h) = 0,$ where $c$ , $g$ and $h$ are real constants and $i = 1, 2, ..., n$ .

Oscillation theorems of comparison type for neutral nonlinear functional differential equations

Said R. Grace — 1995

Czechoslovak Mathematical Journal

Oscillation theorems of comparison type of delay differential equations with a nonlinear damping term

Said R. Grace — 1994

Mathematica Slovaca

Oscillatory behaviour of certain difference equations

Said R. Grace — 2000

Mathematica Slovaca

Oscillation of even order nonlinear functional differential equations with deviating arguments

Said R. Grace — 1991

Mathematica Slovaca

An oscillation criterion for $n$ -th order nonlinear differential equations with retarded arguments

Said R. Grace; Bikkar S. Lalli — 1984

Czechoslovak Mathematical Journal

Oscillation theorems for certain nonlinear differential equations with deviating arguments

Said R. Grace; Bikkar S. Lalli — 1986

Czechoslovak Mathematical Journal

Oscillation theorems for certain neutral differential equations

Said R. Grace; Bikkar S. Lalli — 1988

Czechoslovak Mathematical Journal

Oscillation theorem for a second order nonlinear ordinary differential equation with damping term

Said R. Grace; Bikkar S. Lalli — 1986

Commentationes Mathematicae Universitatis Carolinae

Oscillation theorems for nonlinear second order differential equations with a damping term

Said R. Grace; Bikkar S. Lalli — 1989

Commentationes Mathematicae Universitatis Carolinae

Oscillation criteria for forced neutral differential equations

Said R. Grace; Bikkar S. Lalli — 1994

Czechoslovak Mathematical Journal

On the oscillation of certain neutral difference equations

Said R. Grace; G. G. Hamedani — 2000

Mathematica Bohemica

Various new criteria for the oscillation of nonlinear neutral difference equations of the form i (xn-xn-h)+qn |xn-g|c sgnxn-g=0, i=1,2,3 and c>0, are established.

On the stability of solutions of certain systems of differential equations with piecewise constant argument

Said R. Grace; Mustafa R. S. Kulenović; Hamdy El-Metwally — 2002

Czechoslovak Mathematical Journal

We obtain some sufficient conditions for the existence of the solutions and the asymptotic behavior of both linear and nonlinear system of differential equations with continuous coefficients and piecewise constant argument.

On the oscillation of certain difference equations

Said R. Grace; H. A. El-Morshedy — 2000

Mathematica Bohemica

In this paper we study the oscillation of the difference equations of the form 2xn+pnxn+f(n, xn-g, xn-h)=0, in comparison with certain difference equations of order one whose oscillatory character is known. The results can be applied to the difference equation 2xn+pnxn+qn|xn-g||xn-h|sgnxn-g=0, where $λ$ and $μ$ are real constants, $λ > 0$ and $μ \geq 0$ .

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Currently displaying 1 – 18 of 18

On the oscillation of certain third-order difference equations.

Oscillation criteria for first-order forced nonlinear difference equations.

Linearization and higher order nonlinear oscillation theorems using comparison methods.

Oscillation of certain difference equations

Oscillations of certain functional differential equations

Oscillation theorems of comparison type for neutral nonlinear functional differential equations

Oscillation theorems of comparison type of delay differential equations with a nonlinear damping term

Oscillatory behaviour of certain difference equations

Oscillation of even order nonlinear functional differential equations with deviating arguments

An oscillation criterion for $n$ -th order nonlinear differential equations with retarded arguments

Oscillation theorems for certain nonlinear differential equations with deviating arguments

Oscillation theorems for certain neutral differential equations

Oscillation theorem for a second order nonlinear ordinary differential equation with damping term

Oscillation theorems for nonlinear second order differential equations with a damping term

Oscillation criteria for forced neutral differential equations

On the oscillation of certain neutral difference equations

On the stability of solutions of certain systems of differential equations with piecewise constant argument

On the oscillation of certain difference equations