AAM  >> Vol. 1 No. 1 (August 2012)

    时标上三阶带脉冲的P-Laplacian动力方程边值问题
    Three Order Impulsive Boundary Value Problem with P-Laplacian on Time Scales

  • 全文下载: PDF(186KB) HTML    PP.28-33   DOI: 10.12677/AAM.2012.11004  
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作者:  

齐淑珍:燕山大学理学院,秦皇岛;
杨军:燕山大学理学院,秦皇岛;河北省数学研究中心,石家庄;
齐黎阳:沙河市高村学区辛寨小学,沙河;
程猛:燕山大学电气工程学院,秦皇岛

关键词:
边值问题脉冲不动点定理时标Boundary Value Problem; Impulsive; Fixed Point Theorem; Time Scale

摘要:
本文利用Avery-peterson不动点定理得到了时标上一类带脉冲的P-Laplacian多点边值问题的正解存在性,并且建立了至少存在三个正解的充分条件,为现有的相关结果作了进一步推广,同时为含有带脉冲的P-Laplacian多点边值问题的研究奠定了理论基础,最后给出数字例子对主要结果进行了证明。

This paper uses Avery-Peterson fixed point theorem on cone to study existence of positive solutions for a class of mixed impulsive boundary value problem with P-Laplacian. Some new results for the existence of at least three positive solutions of the boundary value problem are obtained, thus our results make a theoretical foundation for the further study of the impulsive boundary value problem with P-Laplacian. Finally, an example is worked out to demonstrate our results.

文章引用:
齐淑珍, 杨军, 齐黎阳, 程猛. 时标上三阶带脉冲的P-Laplacian动力方程边值问题[J]. 应用数学进展, 2012, 1(1): 28-33. http://dx.doi.org/10.12677/AAM.2012.11004

参考文献

[1] Z. M. He. Double positive solutions of three-point boundary value problems for P-Laplacian dynamic equations on time scales. Journal of Computational and Applied Mathematics, 2005, 182(2): 304-315.
[2] C. X. Song, C. T. Xiao. Positive solutions for P-Laplacian functional dynamic equations on time scales. Nonlinear Analysis, 2007, 66(10): 1989-1998.
[3] M. Benchohra, S. K. Ntouyas and A. Ouahab. Existence results for second order boundary value problem of impulsive dynamic equations on time scales. Journal of Mathematical Analysis and Applications, 2004, 296(1): 65-73.
[4] R. I. Avery, A. C. Peterson. Three positive fixed points of nonlinear operators on ordered banach spaces. Computers & Mathematics with Applications, 2001, 42(3): 313-322.
[5] J. L. Li, J. H. Shen. Existence results for second-order impulsive boundary value problems on time scales. Nonlinear Analysis, 2009, 70: 1648- 1655.