Oscillation Criteria for Second-Order Nonlinear Differential Equations with Damping Term

2003 ◽  
Vol 10 (4) ◽  
pp. 771-784
Author(s):  
Qi-Ru Wang
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Second Order ◽  
Damping Term ◽  
Riccati Technique ◽  
Averaging Technique ◽  
Oscillation Criteria ◽  
Integral Averaging Technique ◽  
Generalized Riccati Technique

Abstract By employing a generalized Riccati technique and an integral averaging technique, new oscillation criteria are established for a class of second-order nonlinear differential equations with damping term. These criteria extend, improve and unify a number of existing results and handle the cases which are not covered by the known criteria. In particular, several interesting examples that illustrate the importance of our results are included.

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.

scholarly journals Integral averaging techniques for the oscillation of second order sublinear ordinarry differential equations

1986 ◽  
Vol 40 (1) ◽  
pp. 111-130 ◽  
Author(s):  
Ch. G. Philos
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Second Order ◽  
Averaging Technique ◽  
Oscillation Criteria ◽  
Integral Averaging Technique ◽  
Special Cases ◽  
Averaging Techniques

AbstractNew oscillation criteria are established for second order sublinear ordinary differential equations with alternating coefficients. These criteria are obtained by using an integral averaging technique and can be applied in some special cases in which other classical oscillation results are no applicable.

scholarly journals Oscillation Properties for Second-Order Partial Differential Equations with Damping and Functional Arguments

2011 ◽  
Vol 2011 ◽  
pp. 1-14
Author(s):  
Run Xu ◽  
Yuhua Lu ◽  
Fanwei Meng
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Averaging Method ◽  
Second Order ◽  
Partial Differential ◽  
Riccati Technique ◽  
Oscillation Criteria ◽  
Generalized Riccati Technique ◽  
High Degree ◽  
Oscillation Properties

Using an integral averaging method and generalized Riccati technique, by introducing a parameterβ≥1, we derive new oscillation criteria for second-order partial differential equations with damping. The results are of high degree of generality and sharper than most known ones.

scholarly journals Oscillation Criteria Based on a New Weighted Function for Linear Matrix Hamiltonian Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-12
Author(s):  
Yingxin Guo ◽  
Junchang Wang
Keyword(s):  
Hamiltonian Systems ◽  
Differential System ◽  
Linear Matrix ◽  
Riccati Technique ◽  
Weighted Function ◽  
Averaging Technique ◽  
Oscillation Criteria ◽  
Integral Averaging Technique ◽  
Generalized Riccati Technique ◽  
Matrix Differential

By employing a generalized Riccati technique and an integral averaging technique, some new oscillation criteria are established for the second-order matrix differential systemU′=A(x)U+B(t)V,V′=C(x)U−A∗(t)V, whereA(t),B(t), andC(t)are(n×n)-matrices, andB,Care Hermitian. These results are sharper than some previous results.

scholarly journals Oscillation Criteria for a Class of Second-Order Nonlinear Differential Equations with Damping Term

2009 ◽  
Vol 2009 ◽  
pp. 1-12 ◽  
Author(s):  
Zigen Ouyang ◽  
Jichao Zhong ◽  
Shuliang Zou
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
New Method ◽  
Damping Term ◽  
Oscillation Criteria

A class of second-order nonlinear differential equations with damping term(r(t)|x′(t)|x′(t))′+p(t)|x′(t)|x′(t)+q(t)f(x(t))=0are investigated in this paper. By using a new method, we obtain some new sufficient conditions for the oscillation of the above equation, and some references are extended in this paper. Examples are inserted to illustrate this result.

scholarly journals Important Criteria for Asymptotic Properties of Nonlinear Differential Equations

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1659
Author(s):  
Ahmed AlGhamdi ◽  
Omar Bazighifan ◽  
Rami Ahmad El-Nabulsi
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Nonlinear Differential Equations ◽  
Asymptotic Properties ◽  
Riccati Technique ◽  
Averaging Technique ◽  
Integral Averaging Technique ◽  
The Subject ◽  
Oscillation Theorems ◽  
New Criteria

In this article, we prove some new oscillation theorems for fourth-order differential equations. New oscillation results are established that complement related contributions to the subject. We use the Riccati technique and the integral averaging technique to prove our results. As proof of the effectiveness of the new criteria, we offer more than one practical example.

scholarly journals Interval criteria for oscillation of second order half-linear differential equations with damping

2005 ◽  
Vol 36 (1) ◽  
pp. 49-56
Author(s):  
Zhiting Xu ◽  
Shiguo Peng
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Linear Differential Equations ◽  
Half Line ◽  
Averaging Technique ◽  
Oscillation Criteria ◽  
Integral Averaging Technique ◽  
Interval Oscillation ◽  
Linear Differential

Interval oscillation criteria are established for second order half-linear differential equations with damping that are different from most known ones in the sense that they are based only on a sequence of subintervals of $ [t_0, \infty)$, rather than on the whole half-line. The results extend the integral averaging technique and include earlier results.

scholarly journals Amended oscillation criteria for second-order neutral differential equations with damping term

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Osama Moaaz ◽  
George E. Chatzarakis ◽  
Thabet Abdeljawad ◽  
Clemente Cesarano ◽  
Amany Nabih
Keyword(s):  
Differential Equations ◽  
Second Order ◽  
Application Area ◽  
Damping Term ◽  
Oscillation Criteria ◽  
Neutral Differential Equations

Abstract The aim of this work is to improve the oscillation results for second-order neutral differential equations with damping term. We consider the noncanonical case which always leads to two independent conditions for oscillation. We are working to improve related results by simplifying the conditions, based on taking a different approach that leads to one condition. Moreover, we obtain different forms of conditions to expand the application area. An example is also given to demonstrate the applicability and strength of the obtained conditions over known ones.

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