共查询到20条相似文献,搜索用时 437 毫秒
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Martin Bohner Olga Karpenko Oleksandr Stanzhytskyi 《Journal of Difference Equations and Applications》2013,19(7):1112-1126
In this paper, we present conditions ensuring that solutions of linear second-order differential equations oscillate, provided solutions of corresponding difference equations oscillate. We also establish the converse result, namely, when oscillation of solutions of difference equations implies oscillation of solutions of corresponding differential equations. 相似文献
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We compute explicitly the oscillation constant for certain half-linear second-order differential equations involving periodic coefficients. If these periodic functions are constants, our results reduce to the well-known oscillation constants for half-linear Euler and Riemann–Weber differential equations. 相似文献
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Xiuxiang Liu 《Applied mathematics and computation》2009,215(1):283-291
Some oscillation criteria for a forced mixed type Emden-Fowler equation with impulses are given. When the impulses are dropped, our results extend those of Sun and Meng [Y.G. Sun, F.W. Meng, Interval criteria for oscillation of second-order differential equations with mixed nonlinearities, Appl. Math. Comput. 15 (2008) 375-381], Sun and Wong [Y.G. Sun, J.S.W. Wong, Oscillation criteria for second order forced ordinary differential equations with mixed nonlinearities, J. Math. Anal. Appl. 334 (2007) 549-560] for second-order forced ordinary differential equation with mixed nonlinearities, Nasr [A.H. Nasr, Sufficient conditions for the oscillation of forced superlinear second order differential equations with oscillatory potential, Proc. Am. Math. Soc. 126 (1998) 123-125], Yang [Q. Yang, Interval oscillation criteria for a forced second order nonlinear ordinary differential equations with oscillatory potential, Appl. Math. Comput. 135 (2003) 49-64] for forced superlinear Emden-Fowler equation, Kong [Q. Kong, Interval criteria for oscillation of second-order linear differential equations, J. Math. Anal. Appl. 229 (1999) 483-492] for unforced second order linear differential equations, and Wong [J.S.W. Wong, Oscillation criteria for a forced second order linear differential equation, J. Math. Anal. Appl. 231 (1999) 235-240] for forced second order linear differential equation. 相似文献
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《Mathematical and Computer Modelling》2004,39(2-3):197-208
This paper is concerned with the oscillation of a class of general type second-order differential equations with nonlinear damping terms. Several new oscillation criteria are established for such a class of differential equations under quite general assumptions. Examples are also given to illustrate the results. 相似文献
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杨甲山 《数学物理学报(A辑)》2014,34(2):393-408
研究了时间测度链上一类具正负系数和阻尼项及非线性中立项的二阶变时滞非线性动力方程的振荡性.利用时间测度链上的有关理论及广义Riccati变换,结合大量不等式技巧,建立了该方程若干新的振动准则,这些准则不仅推广和改进了一些已知的结果,而且在时间测度链上统一了二阶非线性时滞阻尼微分方程和二阶非线性时滞阻尼差分方程的振动性质. 相似文献
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By using the generalized Riccati transformation and the inequality technique, we establish some new oscillation criteria for the second-order nonlinear delay dynamic equations with damping on a time scale. Our results extend and improve some known theorems, but also unify the oscillation of the second-order nonlinear delay differential equation with damping and the second-order nonlinear delay difference equation with damping. 相似文献
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Quanxin Zhang 《Journal of Computational and Applied Mathematics》2011,235(5):1180-1188
By using the generalized Riccati transformation and the inequality technique, we establish a few new oscillation criterions for certain second-order half-linear delay dynamic equations with damping on a time scale. Our results extend and improve some known results, but also unify the oscillation of the second-order half-linear delay differential equation with damping and the second-order half-linear delay difference equation with damping. 相似文献
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This paper is concerned with oscillatory behavior of a class of second-order delay dynamic equations on a time scale. Two new oscillation criteria are presented that improve some known results in the literature. The results obtained are sharp even for the second-order ordinary differential equations. 相似文献
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G. A. Grigoryan 《Differential Equations》2011,47(9):1237-1252
We prove two comparison tests for second-order linear differential equations. The well-known Sturm comparison theorem is a
straightforward corollary of the first of them. The second (integral) test permits one to use specific integral relations
between the coefficients of two equations to prove the oscillation of one of the equations assuming the oscillation of the
other. 相似文献
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In this paper, for all regular solutions of a class of second-order nonlinear perturbed differential equations, new oscillation criteria are established. Asymptotic behavior for forced equations is also discussed. 相似文献
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《Journal of Computational and Applied Mathematics》2007,205(1):231-238
By employing the generalized Riccati technique and the integral averaging technique, new interval oscillation criteria are established for second-order nonlinear differential equations. 相似文献
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《Applied Mathematics Letters》2001,14(1):81-85
We present a new oscillation criterion for a class of second-order nonlinear functional differential equations obtained by using the integral averaging technique. 相似文献
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利用广义Riccati技巧和积分平均技巧,研究具有强迫项的二阶非线性时滞微分方程的振动性态,得到了这类方程振动的若干新的区间判别准则. 相似文献
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M. A. Abdou Khamis I. Mohamed A. S. Ismail 《Journal of Applied Mathematics and Computing》2003,13(1-2):165-182
Sufficient conditions for oscillation of all solutions of a class of second-order quasilinear delay differential equations with fixed moments of impulse effect are found. 相似文献
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John Gregory 《Journal of Mathematical Analysis and Applications》1975,51(3):580-595
The purpose of this paper is to generalize the theory, methods, and results for oscillation of second-order normal ordinary differential equations. This purpose is obtained by use of a theory of quadratic forms on Hilbert spaces given by Hestenes and the author.In particular, the ideas of this paper may be applied to second-order abnormal problems of differential equations, higher-order control problems, integral and partial differential equations, abstract approximation problems, and to finite dimensional approximations which lead to meaningful computer algorithms.For expository purposes some examples are included. Finally we show that specific existence and comparison theorems for the second-order case may be generalized to the 2nth-order case. 相似文献
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We study oscillatory properties of solutions to a class of nonlinear second-order differential equations with a nonlinear damping. New oscillation criteria extend those reported in [ROGOVCHENKO, Yu. V.—TUNCAY, F.: Oscillation criteria for second-order nonlinear differential equations with damping, Nonlinear Anal. 69 (2008), 208–221] and improve a number of related results. 相似文献
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1IntroductionInthepaper,weconsiderthesecond-orderdiferentialequationswithimpulsesas(r(t)x′)′+f(t,x)=0,t≥t0,t≠0,k=1,2,…,x(t+k)... 相似文献