JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (05): 45-50.doi: 10.6040/j.issn.1671-9352.0.2014.361

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Existence of nonoscillatory solutions to second order forced neutral dynamic equations with time delay on time scales

FAN Jin-jun, LU Xiao-dong   

  1. School of Mathematical Science, Shandong Normal University, Jinan 250014, Shandong, China
  • Received:2014-08-07 Online:2015-05-20 Published:2015-05-29

Abstract: The existence of nonoscillatory solutions to a calss of second order forced neutral dynamic equations with time delay on time scales is discussed. The main tool is the Krasnoselskii's fixed point theorem.

Key words: time scales, time delay, neutral, nonoscillatory solution, dynamic equations

CLC Number: 

  • O175.14
[1] AGARWAL R P, BOHNER M. Basic calculus on time scales and some of its applications[J]. Results Math, 1999, 35:3-22.
[2] AGARWAL R P, BOHNER M, O'REGAN D, et al. Dynamic equations on time scales: a survey[J]. J Comput Appl Math, 2002, 141(1/2):1-26.
[3] BOHNER M, PETERSON A. Dynamic equations on time scales. An introduction with applications[M]. Berlin: Birkhauser Boston, 2001.
[4] ERBE L H, KONG Qingkai, ZHANG binggen. Oscillation theory for functional differential equations[M]. New York: Marcel Dekker, 1995.
[5] ERBE L H, PETERSON A. Positive solutions for a nonlinear differential equation on a measure chain[J]. Math Anal Appl, 2002, 275(1):418-438.
[6] HILGER S. Analysis on measure chains-a unified approach to continuous and discrete calculus[J]. Results Math,1990, 18:18-56.
[7] ERBE L H, JIA Baoguo, PETERSON A. Nonoscillation for second order sublinear dynamic equations on time scales[J]. J Comput Appl Math, 2009, 232:594-599.
[8] ZAFER A. On oscillation and nonoscillation of second order dynamic equations[J]. Appl Math Lett, 2009, 22:136-141.
[9] FAN Jinjun, LI Liqing. Existence of positive solutions for p-Laplacian dynamic equations with derivative on time scales[J]. Journal of Applied Mathematics, 2013, 2013:736583.1-736583.7.
[10] 范进军,张雪玲,刘衍胜.时间测度上带p-Laplace算子的m点边值问题正解的存在性[J]. 山东大学学报:理学版, 2012,47(6):16-19. FAN Jinjun, ZHANG Xueling, LIU Yansheng. Existence of positive solutions of nonlinear m-point boundary value problem with p-Laplace operator on time scales[J]. Journal of Shandong University: Natural Science, 2012, 47(6):16-19.
[11] BAINOV D D, MISHEV D P. Oscillation theory for neutral differential equations with delay[M]. New York: Adam Hilger, 1991:1-350.
[12] ZHOU Yong, HUANG Yunqing. Existence of nonoscillatory solutions of second order neutral delay difference equations[J]. J Math Anal Appl, 2001, 20(4):1065-1074.
[13] ERBE L H, HILGER S. Sturmian theory on measure chains[J]. Differential Equations Dynamic Systems, 1993, 1:223-246.
[14] ZHOU Yong. Existence for nonoscillatory solutions of second-order nonlinear differential equations[J]. J Math Anal Appl, 2007, 331(1):91-96.
[15] LI Tongxing, HAN Zhenlai, SUN Shurong, et al. Existence of nonoscillatory solutions to second-order neutral delay dynamic equations on time scales[J]. Advances in Difference Equations, 2009, 2009:562329.01-562329.10.
[16] 高瑾,程世辉,王其如.二阶非线性中立型时标动态方程非振动解的存在性[J]. 中山大学学报:自然科学版,2009,48(6):23-26. GAO Jin, CHENG Shihui, WANG Qiru. Existence of nonoscillatory solutions to second-order nonlinear neutral dynamic equations on time scales[J]. Journal of Zhongshan University: Natural Science, 2009, 48(6):23-26.
[17] AGARWAL R P, BOHNER M, SAKER S H. Oscillation of second order delay dynamic equations[J]. Canadian Applied Mathematics Quarterly, 2005, 13(1):1-18.
[18] ABDALLAH S H. Oscillatory and non-oscillatory behavior of second-order neutral delay equations[J]. Appl Math Comput, 2003, 135:333-344.
[19] AGARWAL R P, BOHNER M, REHAK P. Half-linear dynamic equations[J]. Nonlinear Analysis and Applications, 2003, 1:1-57.
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