scholarly journals New Oscillation Criteria for Third-Order Nonlinear Functional Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Quanxin Zhang ◽  
Li Gao ◽  
Shouhua Liu ◽  
Yuanhong Yu
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Asymptotic Behavior Of Solutions ◽  
Riccati Transformation ◽  
Third Order ◽  
Nonlinear Functional ◽  
Integral Averaging Technique ◽  
Generalized Riccati Transformation ◽  
Functional Differential

This paper discusses oscillatory and asymptotic behavior of solutions of a class of third-order nonlinear functional differential equations. By using the generalized Riccati transformation and the integral averaging technique, three new sufficient conditions which insure that the solution is oscillatory or converges to zero are established. The results obtained essentially generalize and improve the earlier ones.

Oscillatory and Asymptotic Behavior of Third-Order Nonlinear Functional Differential Equations

2013 ◽  
Vol 303-306 ◽  
pp. 1247-1251
Author(s):  
Li Gao ◽  
Yuan Hong Yu ◽  
Quan Xin Zhang
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Asymptotic Behavior Of Solutions ◽  
Third Order ◽  
Nonlinear Functional ◽  
Integral Averaging Technique ◽  
Generalized Riccati Transformation ◽  
Functional Differential

This paper is concerned with oscillatory and asymptotic behavior of solutions of a class of third-order nonlinear functional differential equations. By using the generalized Riccati transformation and the integral averaging technique, two new sufficient conditions which insure that the solution is oscillatory or converges to zero are established. The results obtained essentially generalize and improve earlier ones.

Oscillation Criterion of Third-Order Nonlinear Neutral Damped Functional Differential Equations

2012 ◽  
Vol 204-208 ◽  
pp. 4835-4839
Author(s):  
Yun Hui Zeng
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Oscillation Criterion ◽  
Third Order ◽  
Deviating Arguments ◽  
Integral Averaging Technique ◽  
Generalized Riccati Transformation ◽  
Type Integral ◽  
Functional Differential

In this paper, A class of third-order nonlinear neutral damped functional differential equations with distributed deviating arguments are studied. By using a generalized Riccati transformation and Kamenev-type or Philos-type integral averaging technique,we establish some new sufficient conditions which insure that any solution of this equation oscillates or converges to zero.

scholarly journals Oscillatory Criteria for Higher Order Functional Differential Equations with Damping

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Peiguang Wang ◽  
Hai Cai
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Higher Order ◽  
Riccati Transformation ◽  
Averaging Technique ◽  
Oscillation Criteria ◽  
Integral Averaging Technique ◽  
Generalized Riccati Transformation ◽  
Functional Differential

We investigate a class of higher order functional differential equations with damping. By using a generalized Riccati transformation and integral averaging technique, some oscillation criteria for the differential equations are established.

Asymptotic Behavior for Nonoscillatory Solutions of Second Order Nonlinear Functional Differential Equation

2012 ◽  
Vol 616-618 ◽  
pp. 2137-2141
Author(s):  
Zhi Min Luo ◽  
Bei Fei Chen
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Differential Equations ◽  
Functional Differential Equation ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Nonoscillatory Solutions ◽  
Nonlinear Functional ◽  
Nonlinear Functional Differential Equation ◽  
Functional Differential

This paper studied the asymptotic behavior of a class of nonlinear functional differential equations by using the Bellman-Bihari inequality. We obtain results which extend and complement those in references. The results indicate that all non-oscillatory continuable solutions of equation are asymptotic to at+b as under some sufficient conditions, where a,b are real constants. An example is provided to illustrate the application of the results.

On nonlinear boundary value problems for higher order functional differential equations

2016 ◽  
Vol 23 (4) ◽  
pp. 537-550 ◽  
Author(s):  
Ivan Kiguradze ◽  
Zaza Sokhadze
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Functional Differential Equations ◽  
Nonlocal Boundary ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Nonlinear Boundary Value Problems ◽  
Nonlinear Functional ◽  
Functional Differential

AbstractFor higher order nonlinear functional differential equations, sufficient conditions for the solvability and unique solvability of some nonlinear nonlocal boundary value problems are established.

scholarly journals Asymptotic behavior of solutions of nonlinear functional differential equations

1994 ◽  
Vol 17 (4) ◽  
pp. 703-712
Author(s):  
Jong Soo Jung ◽  
Jong Yeoul Park ◽  
Hong Jae Kang
Keyword(s):  
Differential Equation ◽  
Hilbert Space ◽  
Asymptotic Behavior ◽  
Differential Equations ◽  
Maximal Monotone Operator ◽  
Functional Differential Equations ◽  
Maximal Monotone ◽  
Asymptotic Behavior Of Solutions ◽  
Nonlinear Functional ◽  
Functional Differential

Using the properties of almost nonexpansive curves introduced by B. Djafari Rouhani, we study the asymptotic behavior of solutions of nonlinear functional differential equationdu(t)/dt+Au(t)+G(u)(t)?f(t), whereAis a maximal monotone operator in a Hilbert spaceH,f?L1(0,8:H)andG:C([0,8):D(A)¯)?L1(0,8:H)is a given mapping.

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