时间尺度上三阶Emden-Fowler动力方程的振动准则

Abstract

Abstract:

By means of Riccati transformation technique, the authors establish some new oscillation criteria for the third-order Emden-Fowler delay dynamic equations
(a(t)(r(t)x^? (t))^? ) ^?+p(t)x^γ (τ(t)) = 0
on a time scales , where γ > 0 is a quotient of odd positive integers, a, r, p are real-valued T positive rd-continuous functions defined on . Some new oscillation results which deal with T some cases not covered by existing results in the literature are obtained. Some examples are considered to illustrate the main results.

Key words: Third-order, Delay dynamic equations, Time scales

CLC Number:

39A21

LI Tong-Xin, HAN Zhen-Lai, ZHANG Cheng-Hui, SUN Yi-Bing. Oscillation Criteria for Third-order Emden-Fowler Delay Dynamic Equations on Time Scales[J].Acta mathematica scientia,Series A, 2012, 32(1): 222-232.

Trendmd

References

[1] Hilger S. Analysis on measure chains---a unified approach to continuous and discrete calculus. Results Math, 1990, 18: 18--56

[2] Bohner M, Peterson A. Dynamic Equations on Time Scales: an Introduction with Applications. Boston: Birkh\"{a}user, 2001

[3] Agarwal R P, Bohner M, O'Regan D, Peterson A. Dynamic equations on time scales: a survey. J Comput Appl Math, 2002, 141: 1--26

[4] Bohner M, Peterson A. Advances in Dynamic Equations on Time Scales. Boston: Birkh\"{a}user, 2003

[5] Bohner M. Some oscillation criteria for first order delay dynamic equations. Far East J Appl Math, 2005, 18: 289--304

[6] Zhang B G, Deng X. Oscillation of delay differential equations on time scales. Math Comput Model, 2002, 36:
1307--1318

[7] Zhu Z, Wang Q. Existence of nonoscillatory solutions to neutral dynamic equations on time scales. J Math Anal Appl, 2007, 335: 751--762

[8] 李同兴, 韩振来. 一类具振动系数的二阶中立型差分方程振动性. 济南大学学报(自然科学版), 2009, 23(4): 410--413

[9] 欧柳曼, 朱思铭. 时标动力方程的稳定性分析. 数学物理学报, 2008, 28A(2): 308--319

[10] 陈维松, 韩振来. 几类微分方程解的渐近性. 济南大学学报(自然科学版), 2009, 23(3): 296--298

[11] 赵以阁, 孙书荣. Sturm-Liouville特征值问题. 济南大学学报(自然科学版). 2009, 23(3): 299--301

[12] 曹凤娟, 韩振来. 具偏差变元p-Laplace微分方程周期解存在性. 济南大学学报(自然科学版), 2010, 24(1): 95--98

[13] Erbe L, Peterson A, Saker S H. Oscillation criteria for second-order nonlinear delay dynamic equations. J Math Anal Appl, 2007, 333: 505--522

[14] Grace S R, Agarwal R P, Bohner M, O'Regan D. Oscillation of second-order strongly superlinear and strongly sublinear dynamic equations. Communications in Nonlinear Science and Numerical Simulation, 2009, 14: 3463--3471

[15] Han Z, Sun S, Shi B. Oscillation criteria for a class of second order Emden-Fowler delay dynamic equations on time scales. J Math Anal Appl, 2007, 334: 847--858

[16] \c{S}ahiner Y. Oscillation of second-order delay differential equations on time scales. Nonlinear Analysis, TMA 2005, 63: 1073--1080

[17] Saker S H. Oscillation of nonlinear dynamic equations on time scales. Appl Math Comput, 2004, 148: 81--91

[18] 李同兴, 韩振来. 时间尺度上二阶超线性动力方程振动性. 济南大学学报(自然科学版), 2010, 24(2): 209--211

[19] 王宏洲, 俞元洪. 一阶中立型时滞微分方程的强迫振动. 数学物理学报, 2007, 27A(1): 90--96

[20] 孙一冰, 韩振来, 李同兴. 二阶拟线性中立型动力方程振动准则. 济南大学学报(自然科学版), 2010, 24(3): 308--311

[21] Liu Ailian, Wu Hongwu, Zhu Siming, Ronald M Mathsen. Oscillation for nonautonomous neutral dynamic delay equations on time scales. Acta Mathematica Scientia, 2006, 26B(1): 99--106

[22] 张光荣, 孙书荣. 二阶非线性时滞动力方程的振动性. 济南大学学报(自然科学版), 2010, 24(4): 414--416

[23] Erbe L, Peterson A, Saker S H. Asymptotic behavior of solutions of a third-order nonlinear dynamic equation on time scales. J Comput Appl Math, 2005, 181: 92--102

[24] Erbe L, Peterson A, Saker S H. Hille and Nehari type criteria for third order dynamic equations. J Math Anal Appl, 2007, 329: 112--131

[25] Erbe L, Peterson A, Saker S H. Oscillation and asymptotic behavior a third-order nonlinear dynamic equation. Can Appl Math Q, 2006, 14: 129--147

[26] Erbe L, Hassan T S, Peterson A. Oscillation of third-order functional dynamic equations with mixed
arguments on time scales. J Appl Math Comput, 2010, 34: 353–371

[27] Erbe L, Hassan T S, Peterson A. Oscillation of third order nonlinear functional dynamic equations on time scales. Differ Equ Dyn Syst, 2010, 18: 199--227

[28] Han Z, Li T, Sun S, Cao F. Oscillation criteria for third order nonlinear delay dynamic equations on time scales. Ann Polon Math, 2010, 99: 143--156

[29] Han Z, Li T, Sun S, Zhang C. Oscillation behavior of third-order neutral Emden-Fowler delay dynamic equations on time scales. Adv Diff Eq, 2010, 2010: 1--23

[30] Hassan T S. Oscillation of third order nonlinear delay dynamic equations on time scales. Math Comput Model, 2009, 49: 1573--1586

[31] Li T, Han Z, Sun Y, Zhao Y. Asymptotic behavior of solutions for third-order half-linear delay dynamic equations on time scales. J Appl Math Comput, 2011, 36: 333--346

[32] Li T, Han Z, Sun S, Zhao Y. Oscillation results for third order nonlinear delay dynamic equations on time scales. Bulletin of the Malaysian Mathematical Sciences Society (in press)

[33] Yu Z, Wang Q. Asymptotic behavior of solutions of third-order nonlinear dynamic equations on time scales. J Comput Appl Math, 2009, 225: 531--540

[34] Karpuz B. Unbounded oscillation of higher-order nonlinear delay dynamic equations of neutral type with oscillating coefficients. Electron J Qual Theory Differ Equ, 2009, 34: 1--14

[35] Karpuz B. Asymptotic behaviour of bounded solutions of a class of higher-order neutral dynamic equations. Appl Math Comput, 2009, 215: 2174--2183

Oscillation Criteria for Third-order Emden-Fowler Delay Dynamic Equations on Time Scales

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 12

Metrics

Comments

Recommended 10

[1]	Yang Jiashan, Li Tongxing. Oscillation for a Class of Second-Order Damped Emden-Fowler Dynamic Equations on Time Scales [J]. Acta mathematica scientia,Series A, 2018, 38(1): 134-155.
[2]	Li Zhouhong, Zhang Fengshuo, Cao Jinde, Alsaedi Ahmed, Alsaadi Fuad E. Almost Periodic Solution for a Non-Autonomous Two Species Competitive System with Feedback Controls on Time Scales [J]. Acta mathematica scientia,Series A, 2017, 37(4): 730-750.
[3]	Luo Hua. Spectral Theory of Linear Weighted Sturm-Liouville Eigenvalue Problems [J]. Acta mathematica scientia,Series A, 2017, 37(3): 427-449.
[4]	YANG Jia-Shan. Oscillation Criteria for Second-Order Dynamic Equations with Positive and Negative Coefficients and Damping on Time Scales [J]. Acta mathematica scientia,Series A, 2014, 34(2): 393-408.
[5]	ZHANG Qi. Sign-changing Solutions to Third-order Two-point Boundary Value Problem [J]. Acta mathematica scientia,Series A, 2013, 33(2): 216-223.
[6]	WANG Wu-Sheng, ZHOU Xiao-Liang. A Generalized Pachpatte Type \|Inequality on Time Scales and Application to a Boundary Value Problem [J]. Acta mathematica scientia,Series A, 2012, 32(2): 404-413.
[7]	SANG Yan-Bin, WEI Zhong-Li. Existence of Solutions to a Semipositone Third-order Three-point BVP on Time Scales [J]. Acta mathematica scientia,Series A, 2011, 31(2): 455-465.
[8]	FENG Yao-Ling. The Solutions of Linear Dynamical Equations in Commutative Banach Algebra on Time Scales [J]. Acta mathematica scientia,Series A, 2011, 31(2): 439-446.
[9]	LI Yong-Kun, ZHANG Hong-Tao. Positive Periodic Solutions of Neutral Functional Differential Equations with State Dependent Delays on Time Scales [J]. Acta mathematica scientia,Series A, 2010, 30(3): 730-742.
[10]	LV Xue-Qin, CUI Ming-Gen. A Computational Algorithm for Solving Singular Third-order Boundary-value Problem [J]. Acta mathematica scientia,Series A, 2010, 30(2): 320-326.
[11]	Su Youhui;Li Wantong. Triple Positive Symmetric Solutions of Two-Point BVPs for p-Laplacian Dynamic Equations on Time Scales [J]. Acta mathematica scientia,Series A, 2008, 28(6): 1232-1241.
[12]	Chen Shunqing. The Existence of Multile Positive Solutions for a Class of Third-order p-Laplacian Operator Singular Boundary Value Problems [J]. Acta mathematica scientia,Series A, 2006, 26(5): 794-800.