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Nonoscillation theorems for forced second order non linear differential equations

John R. Graef; Paul W. Spikes — 1975

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

Gli Autori provano alcuni nuovi criteri sufficienti, indipendenti da altri criteri da loro ottenuti in precedenza, perché gli integrali dell'equazione $(a(t)x^{\prime})^{\prime}+q(t)f(x)g(x^{\prime})=r(t)$ siano tutti non oscillatori.

On the behavior of the solutions of $x^{\prime\prime}+q(t)f(x)=r(t)$

John R. Graef; Paul W. Spikes — 1973

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

Si esamina il comportamento asintotico delle soluzioni nel caso che $\lim_{t\to\infty}r(t)/q(t)$ sia positivo e $r(t)/q(t)$ sia monotona.

On the oscillatory behavior of solutions of second order nonlinear differential equations

John R. Graef; Paul W. Spikes — 1986

Czechoslovak Mathematical Journal

Continuability, boundedness, and convergence to zero of solutions of a perturbed nonlinear ordinary differential equation

John R. Graef; Paul W. Spikes — 1995

Czechoslovak Mathematical Journal

Asymptotic behaviour and oscillation of solutions of neutral delay difference equations of arbitrary order

Ethiraju Thandapani; P. Sundaram; John R. Graef; Paul W. Spikes — 1997

Mathematica Slovaca

Classification of nonoscillatory solutions of higher order neutral type difference equations

Ethiraju Thandapani; P. Sundaram; John R. Graef; A. Miciano; Paul W. Spikes — 1995

Archivum Mathematicum

The authors consider the difference equation $Δ^{m} [y_{n} - p_{n} y_{n - k}] + δ q_{n} y_{σ (n + m - 1)} = 0 (*)$ where $m \geq 2$ , $δ = \pm 1$ , $k \in N_{0} = {0, 1, 2, \dots}$ , $Δ y_{n} = y_{n + 1} - y_{n}$ , $q_{n} > 0$ , and ${σ (n)}$ is a sequence of integers with $σ (n) \leq n$ and ${lim}_{n \to \infty} σ (n) = \infty$ . They obtain results on the classification of the set of nonoscillatory solutions of ( $*$ ) and use a fixed point method to show the existence of solutions having certain types of asymptotic behavior. Examples illustrating the results are included.

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Currently displaying 1 – 10 of 10

Nonoscillation theorems for forced second order non linear differential equations

On the behavior of the solutions of $x^{\prime\prime}+q(t)f(x)=r(t)$

On the oscillatory behavior of solutions of second order nonlinear differential equations

Continuability, boundedness, and convergence to zero of solutions of a perturbed nonlinear ordinary differential equation

Asymptotic behaviour and oscillation of solutions of neutral delay difference equations of arbitrary order

Classification of nonoscillatory solutions of higher order neutral type difference equations

Boundedness and asymptotic behavior of solutions of a forced difference equation.

On the positive solutions of a higher order functional differential equation with a discontinuity.

Oscillation of a higher order neutral difference equation with a forcing term.

Nonoscillation theorems for functional differential equations of arbitrary order.