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.

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 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 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 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 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.

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 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.

scholarly journals Oscillation Criteria for Second Order Neutral Differential Equations

1996 ◽  
Vol 48 (4) ◽  
pp. 871-886 ◽  
Author(s):  
Horng-Jaan Li ◽  
Wei-Ling Liu
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Second Order ◽  
Neutral Delay ◽  
Oscillation Criteria ◽  
Neutral Differential Equations ◽  
Neutral Delay Differential Equation ◽  
Image Position ◽  
Delay Differential

AbstractSome oscillation criteria are given for the second order neutral delay differential equationwhere τ and σ are nonnegative constants, . These results generalize and improve some known results about both neutral and delay differential equations.

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