一类二阶中立型方程解的振动准则及应用
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摘要
本文研究了一类具有连续偏差变元的二阶中立型方程解的振动性问题,给出上述方程解振动的判别准则.作为应用,我们讨论了一类双曲方程在边界条件下的振动问题.
In this paper, we investigate a class of second order neutral equations with distributed deviating argumens, and obtain oscillatory criteria for such equations. As application, the following hyperbolic equations of neutral type and boundary conditions of the following types is investigated, and some oscillation criteria for such equations satisfying two kinds of boundary conditions are obtained.
In this paper, we investigate a class of second order neutral equations with distributed deviating argumens, and obtain oscillatory criteria for such equations. As application, the following hyperbolic equations of neutral type and boundary conditions of the following types is investigated, and some oscillation criteria for such equations satisfying two kinds of boundary conditions are obtained.
引文
[1]郑祖庥,泛函微分方程理论.合肥：安徽教育出版社.1996.
[2]J.K.Hale, Theory of Functional Differential Equations. New York, Springer, 1977.
[3]Ladde, Lakshmikanthan & Zhang Oscillation Theory of Differential Equations with Deviating Arguments. New York:Marcel Dekker,1987.
[4]D.D. Bainov, D.P. Mishev, Oscillation Theory for Neutral Differential Equations with Delay. New York:Adam Hilger,1991.
[5]L.H.Erbe, Q.K.Kong & B.G.Zhang, Oscillation Theory for Functional Differen-tial Equations. New York:Marcel Dekker,1995.
[6]R.P.Agarwal, S.R.Grace & D.O'Regan, Oscillation Theory for second order dy-namic equations. Talyor & Francis, New York,2003.
[7]J.H. Wu, Theory and Applications of Partial Functional Differential Equations. New York, Springer,1996.
[8]Y.H.Yu, X.L.Fu, Oscillation of Second Order Nonlinear Neutral Equation with Continuous Distributed Deviating Argument. Rad. Mat.,7(1991):167-176.
[9]D.Bainov, V.Petrov, Asymptotic properties of the nonoscillatory solutions of second-order neutral equations with a deviating argument. J. Math. Anal. Appl,190(1995):645-653.
[10]M.K.Grammatikopoulos, G.Ladas & A.Meimaridou, Oscillations of Second or-der neutral delay differential equations. Rad. Mat.,1(1985):267-274.
[11]S.R.Grace, B.S.Lalli, Oscillation of solutions of nonlinear neutral second order delay differential equations Rad. Mat.,3(1987):77-84.
[12]S.Ruan, Oscillations of second neutral differential equations. Canad. Math. Bull.36,4(1993):485-496.
[13]H.J.Li, W.L.Liu, Oscillation creteria for second order neutral differential equa-tions. Can. J. Math.,48,4(1996):871-886.
[14]K.Tanaka, Oscillation properties of solutions of second order neutral differential equations with deviating arguments. Analysis,19,1(1991):99-111.
[15]L.Q. Zhang and X.L. Fu, A class of second order functional differential inequal-ities. Ann. of Diff. Eqs.,12,1(1996):129-136.
[16]P.G.Wang, Y.H.Yu, Oscillation of second order neutral equations with deviating arguments. Math.J.Toyama Univ.,21(1998):55-66.
[17]P.G.Wang, Y.H.Yu, Oscillation of solutions for nonlinear second order neutral equations with deviating arguments. Math. Slovaca.,51,2(2001):205-213.
[18]W.Y.Shi, P.G.Wang, Oscillatory criteria of a class of second-order neutral func-tional differential equations. Appl.Math.Comput,146,1(2003):211-226.
[19]P.G.Wang, X.W.Li, Further results on oscillation of a class of second-order neu-tral equations. J.Comput.Appl.Math.,157,2(2003):407-418.
[20]K. Kreith, T.Kusano & N. Yoshida, Oscillation properties of nonlinear hyper-bolic equations. SIAM J.Math Anal.,15(1984):570-578.
[21]B.S. Lalli, Y.H. Yu & B.T. Cui, Oscillations of certain partial differential equa-tions with deviating arguments. Bull. Austral. Math. Soc.,46(1992):373-380.
[22]B.S. Lalli, Y.H. Yu & B.T. Cui, Forced oscillations of the hyperbolic differential equations with deviating arguments. Indian J. Pure Appl. Math.,25,4(1995):387-397.
[23]D.Bainov, B.T.Cui & E.Minchev, Oscillation properties of the solutions of hy-perbolic equations with deviating arguments. Demon. Math.,29,1(1996):61-68.
[24]X.Z. Liu, X.L. Fu., Oscillation criteria for nonlinear inhomogeous hyperbolic equations with distributed deviating arguments. J. Appl. Math. Stochas. Anal., 1(1996):21-31.
[25]P.G.Wang, Y.H.Yu, Oscillation of a class of hyperbolic boundary value problem. Appl. Math. Letter,10,7(1999):91-98.
[26]V.S.Vladimirov, Equations of Mathematical Physics. Nauka, Moscow,1981.
[2]J.K.Hale, Theory of Functional Differential Equations. New York, Springer, 1977.
[3]Ladde, Lakshmikanthan & Zhang Oscillation Theory of Differential Equations with Deviating Arguments. New York:Marcel Dekker,1987.
[4]D.D. Bainov, D.P. Mishev, Oscillation Theory for Neutral Differential Equations with Delay. New York:Adam Hilger,1991.
[5]L.H.Erbe, Q.K.Kong & B.G.Zhang, Oscillation Theory for Functional Differen-tial Equations. New York:Marcel Dekker,1995.
[6]R.P.Agarwal, S.R.Grace & D.O'Regan, Oscillation Theory for second order dy-namic equations. Talyor & Francis, New York,2003.
[7]J.H. Wu, Theory and Applications of Partial Functional Differential Equations. New York, Springer,1996.
[8]Y.H.Yu, X.L.Fu, Oscillation of Second Order Nonlinear Neutral Equation with Continuous Distributed Deviating Argument. Rad. Mat.,7(1991):167-176.
[9]D.Bainov, V.Petrov, Asymptotic properties of the nonoscillatory solutions of second-order neutral equations with a deviating argument. J. Math. Anal. Appl,190(1995):645-653.
[10]M.K.Grammatikopoulos, G.Ladas & A.Meimaridou, Oscillations of Second or-der neutral delay differential equations. Rad. Mat.,1(1985):267-274.
[11]S.R.Grace, B.S.Lalli, Oscillation of solutions of nonlinear neutral second order delay differential equations Rad. Mat.,3(1987):77-84.
[12]S.Ruan, Oscillations of second neutral differential equations. Canad. Math. Bull.36,4(1993):485-496.
[13]H.J.Li, W.L.Liu, Oscillation creteria for second order neutral differential equa-tions. Can. J. Math.,48,4(1996):871-886.
[14]K.Tanaka, Oscillation properties of solutions of second order neutral differential equations with deviating arguments. Analysis,19,1(1991):99-111.
[15]L.Q. Zhang and X.L. Fu, A class of second order functional differential inequal-ities. Ann. of Diff. Eqs.,12,1(1996):129-136.
[16]P.G.Wang, Y.H.Yu, Oscillation of second order neutral equations with deviating arguments. Math.J.Toyama Univ.,21(1998):55-66.
[17]P.G.Wang, Y.H.Yu, Oscillation of solutions for nonlinear second order neutral equations with deviating arguments. Math. Slovaca.,51,2(2001):205-213.
[18]W.Y.Shi, P.G.Wang, Oscillatory criteria of a class of second-order neutral func-tional differential equations. Appl.Math.Comput,146,1(2003):211-226.
[19]P.G.Wang, X.W.Li, Further results on oscillation of a class of second-order neu-tral equations. J.Comput.Appl.Math.,157,2(2003):407-418.
[20]K. Kreith, T.Kusano & N. Yoshida, Oscillation properties of nonlinear hyper-bolic equations. SIAM J.Math Anal.,15(1984):570-578.
[21]B.S. Lalli, Y.H. Yu & B.T. Cui, Oscillations of certain partial differential equa-tions with deviating arguments. Bull. Austral. Math. Soc.,46(1992):373-380.
[22]B.S. Lalli, Y.H. Yu & B.T. Cui, Forced oscillations of the hyperbolic differential equations with deviating arguments. Indian J. Pure Appl. Math.,25,4(1995):387-397.
[23]D.Bainov, B.T.Cui & E.Minchev, Oscillation properties of the solutions of hy-perbolic equations with deviating arguments. Demon. Math.,29,1(1996):61-68.
[24]X.Z. Liu, X.L. Fu., Oscillation criteria for nonlinear inhomogeous hyperbolic equations with distributed deviating arguments. J. Appl. Math. Stochas. Anal., 1(1996):21-31.
[25]P.G.Wang, Y.H.Yu, Oscillation of a class of hyperbolic boundary value problem. Appl. Math. Letter,10,7(1999):91-98.
[26]V.S.Vladimirov, Equations of Mathematical Physics. Nauka, Moscow,1981.