一类具有扩散系数和连续偏差变元的中立型偶阶偏泛函微分方程的振动性

doi:10.7523/j.issn.2095-6134.2012.6.003

中国科学院大学学报 ›› 2012, Vol. ›› Issue (6): 738-742.DOI: 10.7523/j.issn.2095-6134.2012.6.003

一类具有扩散系数和连续偏差变元的中立型偶阶偏泛函微分方程的振动性

林文贤

韩山师范学院数学与应用数学系, 广东潮州 521041

收稿日期:2011-06-20 修回日期:2012-01-19 发布日期:2012-11-15
通讯作者: 林文贤

Oscillation of a class of even-order neutral partial functional differential equations with continuous deviating arguments and diffusion coefficients

LIN Wen-Xian

Department of Mathematics and Applied Mathematics, Hanshan Normal University, Chaozhou 521041, Guangdong, China

Received:2011-06-20 Revised:2012-01-19 Published:2012-11-15

摘要/Abstract

摘要： 研究一类具有连续偏差变元和非线性扩散系数的偶阶中立型偏泛函微分方程的振动性. 借助广义Riccati变换和微分不等式,获得这类方程分别在Robin和Dirichlet边值条件下所有解振动的若干新的充分性条件,表明其振动是由时滞量引起的. 所得结果推广了最近文献的相关结果.

关键词: 非线性扩散系数, 偏泛函微分方程, 振动性, 广义Riccati变换

Abstract: Oscillation of a class of even-order neutral partial functional differential equations with continuous deviating arguments and nonlinear diffusion coefficients is studied. By employing the generalized Riccati transformation and the differential inequalities, some new sufficient conditions for oscillation of all the solutions of such equations are obtained under Robin and Dirichlet boundary value conditions. The results show that the oscillation is caused by delay. The results generalize some recently published results.

Key words: nonlinear diffusion coefficient, partial functional differential equation, oscillation, generalized Riccati transformation

中图分类号:

O175.27

林文贤. 一类具有扩散系数和连续偏差变元的中立型偶阶偏泛函微分方程的振动性[J]. 中国科学院大学学报, 2012, (6): 738-742.

LIN Wen-Xian. Oscillation of a class of even-order neutral partial functional differential equations with continuous deviating arguments and diffusion coefficients[J]. , 2012, (6): 738-742.

参考文献

[1] Lin S Z, Zhou Z X, Yu Y H. Oscillation criteria for a class of Hyperbolic differential equations continuous distributed deviating arguments[J]. J of Math(PRC), 2005,25 (5): 521-526.
[2] Misher D P. Necessary and sufficient conditions for oscillation of neutral type parabolic differential equations[J]. Comptes Kendus Acad Bulg Sci, 1991,44(3):11-15.
[3] Yoshida N. On the zeros of solutions of hyperbolic equations of neutral type[J]. Differential and Integral Equtions, 1990,3:155-160.
[4] Luo L P. Oscillation theorems of nonlinear neutral hyperbolic partial functional differential equations[J]. J of Math(PRC), 2010, 30(6):1023-1028 (in Chinese). 罗李平. 非线性中立双曲型偏泛函微分方程的振动性定理[J].数学杂志,2010,30(6):1023-1028.
[5] Lin W X. Oscillation theorems of a class of higher order neutral partial differential equations[J]. Journal of Southwest China Normal University, 1998,23(1):25-30 (in Chinese). 林文贤. 一类高阶中立型偏微分方程的振动性[J]. 西南师范大学学报,1998,23(1):25-30.
[6] Lin W X. Oscillation of solutions of high order nonlinear neutral partial differential equations[J]. Journal of Biomathematics, 2003,18(1): 8-14 (in Chinese). 林文贤. 高阶非线性中立型偏微分方程解的振动性[J].生物数学学报,2003,18(1): 8-14.
[7] Lin W X. Oscillation of a class of high order neutral partial functional differential equations[J]. Journal of Heilongjiang University: Natural Science, 2006,23(4):25-30 (in Chinese). 林文贤.一类高阶中立型偏泛函微分方程的振动性[J].黑龙江大学学报:自然科学版,2006,23(4):25-30.
[8] Lin W X. Oscillation theorems of certain neutral hyperbolic differential equations[J]. Mathematica Applicata, 2009, 22(3): 514-519 (in Chinese). 林文贤.一类中立型双曲微分方程的振动性定理[J].应用数学,2009, 22(3):514-519.
[9] Agarwal R P, Grace S R, O'Regan D. Oscillation theory for differential equations[M]. Dordrecht: Kluwer Academic, 2000.
[10] Philos C G. A new criteria for the oscillation and asymptotic behavior of delay differential equations[J]. Bull Acad Pol Sci Ser Sci Mat, 1981, 39(1):61-64.
[11] Vladimirov V S. Equations of mathematical physics[M]. Moscow: Nauka,1981.

一类具有扩散系数和连续偏差变元的中立型偶阶偏泛函微分方程的振动性

Oscillation of a class of even-order neutral partial functional differential equations with continuous deviating arguments and diffusion coefficients

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