NONOSCILLATION RESULTS FOR A CLASS OF THIRD ORDER NONLINEAR DIFFERENTIAL EQUATIONS

Applied Mathematics and Mechanics (English Edition) ›› 2002, Vol. 23 ›› Issue (10): 1170-1175.

NONOSCILLATION RESULTS FOR A CLASS OF THIRD ORDER NONLINEAR DIFFERENTIAL EQUATIONS

Pakize Temtek¹, Aydin Tiryaki²

1. Department of Mathematics, Faculty of Arts and Science, Erciyes University, 38039, Kayseri, Turkey;
2. Department of Mathematics, Faculty of Arts and Science, Gazi University, Teknikokullar 06500 Ankara, Turkey

收稿日期:2001-08-28 出版日期:2002-10-18 发布日期:2002-10-18

NONOSCILLATION RESULTS FOR A CLASS OF THIRD ORDER NONLINEAR DIFFERENTIAL EQUATIONS

Pakize Temtek¹, Aydin Tiryaki²

1. Department of Mathematics, Faculty of Arts and Science, Erciyes University, 38039, Kayseri, Turkey;
2. Department of Mathematics, Faculty of Arts and Science, Gazi University, Teknikokullar 06500 Ankara, Turkey

Received:2001-08-28 Online:2002-10-18 Published:2002-10-18

摘要/Abstract

摘要： Sufficient conditions for the nonoscillatory solutions of a class of third order nonlinear differential equations are presented. The results obtained generalize some criteria given by Parhi. In some special cases, some of these results contain weaker conditions.

关键词: differential equation, nonlinear, nonoscillatory solution, Parhi criteria

Abstract: Sufficient conditions for the nonoscillatory solutions of a class of third order nonlinear differential equations are presented. The results obtained generalize some criteria given by Parhi. In some special cases, some of these results contain weaker conditions.

Key words: differential equation, nonlinear, nonoscillatory solution, Parhi criteria

中图分类号:

O175.12

Pakize Temtek;Aydin Tiryaki. NONOSCILLATION RESULTS FOR A CLASS OF THIRD ORDER NONLINEAR DIFFERENTIAL EQUATIONS[J]. Applied Mathematics and Mechanics (English Edition), 2002, 23(10): 1170-1175.

参考文献

[1] Greguš M.Third Order Linear Differential Equ ations[M].Dordrecht,Boston,Lancaster:D Reidel Publishing Company,1987.
[2] Swanson C A.Comparison and Oscillation Theory of Linear Differential Equations[M].New York:A P,1968.
[3] Birkhoff G D.On solutions of the ordinary linear differential equations of the third order[J].Ann Math,1911,12:103-127.
[4] Gregu M.On some properties of the solutions of a homogeneous linear differential equation of the third order[J].Mat Fiz Casopis Slovensk Akad Vied,1955,5:73-78.
[5] Hanan M.Oscillation criteria for third order linear differential equations[J].Pacific J Math,1961,11:919-944.
[6] Philos Ch G.Oscillation and asymptotic behaviour of third order differential equations[J].Bull Inst Math Acad Sinica,1983,11(2):141-160.
[7] Parhi N.Nonoscillation of solutions of a class of third order differential equations[J].Acta Math Hun gar,1989,54(1-2):79-88.
[8] Cecchi M,D sl Z,Marini M.On the qualitative behaviour of solutions of third order differential equations[J].J Math Anal Appl,1996,197(3):749-766.
[9] Erbe L.Existence of oscillatory solutions and asymptotic behaviour for a class of third order linear differential equations[J].Pacific J Math,1976,64(2):369-385.
[10] Heidel J W.Qualitative behaviour of solutions of a third order nonlinear differential equation[J].Pacific J Math,1968,27:507-526.
[11] Parhi N.Nonoscillatory behaviour of solutions of nonhomogeneous third order differential equations[J].Applicable Analysis,1981,12(4):273-285.
[12] Parhi N,Parhi S.Oscillation and nonoscillation theorems for nonhomogeneous third order diff erential equations[J].Bulletin Inst Math Academia Sinica,1983,11(2):125-139.
[13] Parhi N,Parhi S.Nonoscillation and asymptotic behaviour for forced nonlinear third order diff erential equations[J].Bulletin Inst Math Academia Sinica,1985,13(4):367-384.
[14] Parhi N,Parhi S.On the behaviour solutions of the differential equations(r(t)y")'+q(t)y'^β+p(t)y^α=f(t)[J].Annales Polonici Mathematici,1986,47(2):137-148.
[15] Parhi N,Parhi S.Qualitative behaviour of solutions of f orced nonlinear third order differentialequations[J].Riv Math Univ Parma,1987,13(4):201-210.

NONOSCILLATION RESULTS FOR A CLASS OF THIRD ORDER NONLINEAR DIFFERENTIAL EQUATIONS

NONOSCILLATION RESULTS FOR A CLASS OF THIRD ORDER NONLINEAR DIFFERENTIAL EQUATIONS

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价

[1]	Hongyan CHEN, Youcheng ZENG, Hu DING, Siukai LAI, Liqun CHEN. Dynamics and vibration reduction performance of asymmetric tristable nonlinear energy sink[J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(3): 389-406.
[2]	M. ABBASI GAVARI, M. R. HOMAEINEZHAD. Nonlinear dynamic modeling of planar moving Timoshenko beam considering non-rigid non-elastic axial effects[J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(3): 479-496.
[3]	Runqing CAO, Zilong GUO, Wei CHEN, Huliang DAI, Lin WANG. Nonlinear dynamics of a circular curved cantilevered pipe conveying pulsating fluid based on the geometrically exact model[J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(2): 261-276.
[4]	Yong WANG, Peili WANG, Haodong MENG, Liqun CHEN. Dynamic performance and parameter optimization of a half-vehicle system coupled with an inerter-based X-structure nonlinear energy sink[J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(1): 85-110.
[5]	Xiaoye MAO, Jiabin WU, Junning ZHANG, Hu DING, Liqun CHEN. Dirac method for nonlinear and non-homogenous boundary value problems of plates[J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(1): 15-38.
[6]	Yang JIN, Tianzhi YANG. Enhanced vibration suppression and energy harvesting in fluid-conveying pipes[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(9): 1487-1496.
[7]	Hu DING, J. C. JI. Vibration control of fluid-conveying pipes: a state-of-the-art review[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(9): 1423-1456.
[8]	Guangdong SUI, Shuai HOU, Xiaofan ZHANG, Xiaobiao SHAN, Chengwei HOU, Henan SONG, Weijie HOU, Jianming LI. A bio-inspired spider-like structure isolator for low-frequency vibration[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(8): 1263-1286.
[9]	J. WU, S. F. WANG, P. PERDIKARIS. A dive into spectral inference networks: improved algorithms for self-supervised learning of continuous spectral representations[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(7): 1199-1224.
[10]	Xuhui MENG. Variational inference in neural functional prior using normalizing flows: application to differential equation and operator learning problems[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(7): 1111-1124.
[11]	Ying MENG, Xiaoye MAO, Hu DING, Liqun CHEN. Nonlinear vibrations of a composite circular plate with a rigid body[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(6): 857-876.
[12]	Shengtao ZHANG, Jiaxi ZHOU, Hu DING, Kai WANG, Daolin XU. Fractional nonlinear energy sinks[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(5): 711-726.
[13]	Jian'en CHEN, Jianling LI, Minghui YAO, Jun LIU, Jianhua ZHANG, Min SUN. Nonreciprocity of energy transfer in a nonlinear asymmetric oscillator system with various vibration states[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(5): 727-744.
[14]	Yunping ZHAO, Xiuhui HOU, Kai ZHANG, Zichen DENG. Symplectic analysis for regulating wave propagation in a one-dimensional nonlinear graded metamaterial[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(5): 745-758.
[15]	Jihou YANG, Weixing ZHANG, Xiaodong YANG. Integrated device for multiscale series vibration reduction and energy harvesting[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(12): 2227-2242.