scholarly journals A New Oscillation Criterion for Forced Second-Order Quasilinear Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
Shao Jing
Keyword(s):  
Differential Equation ◽  
Variational Principle ◽  
Differential Equations ◽  
Second Order ◽  
Oscillation Criterion ◽  
Generalized Variational Principle ◽  
Quasilinear Differential Equation ◽  
Riccati Technique ◽  
Forcing Term

By using the generalized variational principle and Riccati technique, a new oscillation criterion is established for second-order quasilinear differential equation with an oscillatory forcing term, which improves and generalizes some of new results in the literature.

scholarly journals Generalized Variational Oscillation Principles for Second-Order Differential Equations with Mixed-Nonlinearities

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Jing Shao ◽  
Fanwei Meng ◽  
Xinqin Pang
Keyword(s):  
Differential Equation ◽  
Variational Principle ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Second Order ◽  
Generalized Variational Principle ◽  
Riccati Technique ◽  
Oscillation Criteria ◽  
Second Order Differential Equations ◽  
Mixed Nonlinearities

Using generalized variational principle and Riccati technique, new oscillation criteria are established for forced second-order differential equation with mixed nonlinearities, which improve and generalize some recent papers in the literature.

scholarly journals Generalized Variational Principles on Oscillation for Nonlinear Nonhomogeneous Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Jing Shao ◽  
Fanwei Meng
Keyword(s):  
Differential Equation ◽  
Variational Principle ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Variational Principles ◽  
Second Order ◽  
Generalized Variational Principle ◽  
Riccati Technique ◽  
Oscillation Criteria ◽  
Order Nonlinear Differential Equation

Using the generalized variational principle and the Riccati technique, new oscillation criteria are established for the forced second-order nonlinear differential equation, which improves and generalizes some of the new results in literature.

Oscillation of Second-Order Nonlinear Differential Equations

2014 ◽  
Vol 548-549 ◽  
pp. 1007-1010
Author(s):  
Qing Zhu ◽  
Zhi Bin Ma
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Nonlinear Differential Equations ◽  
Second Order ◽  
Oscillation Criterion ◽  
Order Nonlinear Differential Equation

A new oscillation criterion is established for a certain class of second-order nonlinear differential equation x"(t)-b(t)x'(t)+c(t)g(x)=0, x"(t)+c(t)g(x)=0 that is different from most known ones. Some applications of the result obtained are also presented. Our results are sharper than some previous ones.

A Second Order Superlinear Oscillation Criterion

1984 ◽  
Vol 27 (1) ◽  
pp. 102-112 ◽  
Author(s):  
Ch. G. Philos
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Second Order ◽  
Oscillation Criterion ◽  
Oscillation Result ◽  
Special Case

AbstractA new oscillation criterion is given for general superlinear ordinary differential equations of second order of the form x″(t)+ a(t)f[x(t)]=0, where a ∈ C([t0∞,)), f∈C(R) with yf(y)>0 for y≠0 and and f is continously differentiable on R-{0} with f'(y)≥0 for all y≠O. In the special case of the differential equation (γ > 1) this criterion leads to an oscillation result due to Wong [9].

scholarly journals Set of Oscillation Criteria for Second Order Nonlinear Forced Differential Equations with Damping

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Ambarka Abdalla Salhin ◽  
Ummul Khair Salma Din ◽  
Rokiah Rozita Ahmad ◽  
Mohd Salmi Md Noorani
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Second Order ◽  
Riccati Technique ◽  
Averaging Technique ◽  
Oscillation Criteria ◽  
Integral Averaging Technique ◽  
Generalized Riccati Technique

By employing a generalized Riccati technique and an integral averaging technique, some new oscillation criteria are established for the second order nonlinear forced differential equation with damping. These results extend, improve, and unify some known oscillation criteria in the existing literature.

Nonprincipal solutions in oscillation criteria for half-linear differential equations

2010 ◽  
Vol 47 (1) ◽  
pp. 127-137
Author(s):  
Ondřej Došlý ◽  
Jana Řezníčková
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Second Order ◽  
Oscillation Criterion ◽  
Linear Differential Equations ◽  
Integral Term ◽  
Oscillation Criteria ◽  
Second Order Differential Equation ◽  
Linear Differential

We establish a new oscillation criterion for the half-linear second order differential equation \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$(r(t)\Phi (x'))' + c(t)\Phi (x) = 0,\Phi (x): = |x|^{p - 2} x,p > 1.$$ \end{document} In this criterion, an integral term appears which involves a nonprincipal solution of a certain equation associated with (*).

scholarly journals Use of the Modified Riccati Technique for Neutral Half-Linear Differential Equations

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 235
Author(s):  
Zuzana Pátíková ◽  
Simona Fišnarová
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Type Equation ◽  
Second Order ◽  
Linear Differential Equations ◽  
Riccati Technique ◽  
Oscillation Criteria ◽  
Type Criterion ◽  
Linear Differential

We study the second-order neutral half-linear differential equation and formulate new oscillation criteria for this equation, which are obtained through the use of the modified Riccati technique. In the first statement, the oscillation of the equation is ensured by the divergence of a certain integral. The second one provides the condition of the oscillation in the case where the relevant integral converges, and it can be seen as a Hille–Nehari-type criterion. The use of the results is shown in several examples, in which the Euler-type equation and its perturbations are considered.

Conjugacy of half-linear second-order differential equations

2000 ◽  
Vol 130 (3) ◽  
pp. 517-525 ◽  
Author(s):  
Ondřej Došlý ◽  
Árpád Elbert
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Focal Point ◽  
Second Order ◽  
Oscillation Criterion ◽  
Riccati Transformation ◽  
Second Order Differential Equations ◽  
Generalized Riccati Transformation ◽  
Image Position

Focal point and conjugacy criteria for the half-linear second-order differential equation are obtained using the generalized Riccati transformation. An oscillation criterion is given in case when the function c(t) is periodic.

scholarly journals Non-Linear Neutral Differential Equations with Damping: Oscillation of Solutions

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 285
Author(s):  
Saad Althobati ◽  
Jehad Alzabut ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Oscillatory Behavior ◽  
Order Equation ◽  
Second Order ◽  
Riccati Technique ◽  
Neutral Equations ◽  
Neutral Differential Equations ◽  
Main Equation ◽  
Non Linear ◽  
Even Order

The oscillation of non-linear neutral equations contributes to many applications, such as torsional oscillations, which have been observed during earthquakes. These oscillations are generally caused by the asymmetry of the structures. The objective of this work is to establish new oscillation criteria for a class of nonlinear even-order differential equations with damping. We employ different approach based on using Riccati technique to reduce the main equation into a second order equation and then comparing with a second order equation whose oscillatory behavior is known. The new conditions complement several results in the literature. Furthermore, examining the validity of the proposed criteria has been demonstrated via particular examples.

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