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.
LIN Wen-Xian
. Oscillation of a class of even-order neutral partial functional differential equations with continuous deviating arguments and diffusion coefficients[J]. Journal of University of Chinese Academy of Sciences, 2012
, (6)
: 738
-742
.
DOI: 10.7523/j.issn.2095-6134.2012.6.003
[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.
