您的位置：山东大学 -> 科技期刊社 -> 《山东大学学报（理学版）》

山东大学学报（理学版） ›› 2017, Vol. 52 ›› Issue (12): 72-80.doi: 10.6040/j.issn.1671-9352.0.2017.312

• • 上一篇    下一篇

带p(t)-Laplacian算子的分数阶微分方程共振无穷多点边值问题解的存在性

张迪,刘文斌*   

  1. 中国矿业大学数学学院, 江苏 徐州 221116
  • 收稿日期:2017-06-20 出版日期:2017-12-20 发布日期:2017-12-22
  • 通讯作者: 刘文斌(1960— ),男,教授,研究方向为常微分方程和非线性泛函分析的理论及应用研究. E-mail:wblium@163.com E-mail:18361273335@163.com
  • 作者简介:张迪(1992— ),女,硕士研究生,研究方向为微分方程边值问题研究. E-mail:18361273335@163.com
  • 基金资助:
    国家自然科学基金资助项目(11271364)

Existence of solutions for p(t)-Laplacian fractional infinite-point boundary value problems at resonance

ZHANG Di, LIU Wen-bin*   

  1. School of Mathematics, China University of Mining and Technology, Xuzhou 221116, Jiangsu, China
  • Received:2017-06-20 Online:2017-12-20 Published:2017-12-22

PDF (PC)

487

摘要： 讨论了一类带p(t)-Laplacian算子的分数阶微分方程共振无穷多点边值问题,通过对非线性项的合理控制,利用Mawhin连续定理得到了解的存在性。

关键词: 边值问题, p(t)-Laplacian算子, 无穷多点, 分数阶微分方程, Mawhin连续定理

Abstract: By using Mawhins continuation theorem, through the reasonable control of the nonlinear term, an existence result for the solutions of fractional infinite-point boundary value problems at resounce with p(t)-Laplacian operator is presented.

Key words: boundary value problem, infinite-point, p(t)-Laplacian operator, fractional differential equation, Mawhins continuation theorem

中图分类号: 

  • O175.8
[1] ZHANG Xingqiu, ZHONG Qiuyan. Multiple positive solutions for nonlocal boundary value problems of singular fractional differential equations[J]. Boundary Value Problems, 2016, 2016(1):1-11.
[2] JIA Mei, ZHANG Haibin, CHEN Qiang. Existence of positive solutions for fractional differential equation with integral boundary conditions on the half-line[J]. Boundary Value Problems, 2016, 2016(1):1-16.
[3] JIA Mei, LIU Xiping. Multiplicity of solutions for integral boundary value problems of fractional differential equations with upper and lower solutions[J]. Applied Mathematics and Computation, 2014, 232:313-323.
[4] 郑春华,刘文斌.一类具有时滞的分数阶微分方程边值问题正解的存在性[J]. 山东大学学报(理学版),2015, 50(3):73-79. ZHEN Chunhua, LIU Wenbin. Existence of positive solutions of the boundary value problem for a class of fractional differential equations w ith delay[J]. Journal of Shandong University(Natural Science), 2015, 50(3):73-79.
[5] XIE Wenzhe, XIAO Jing, LUO Zhiguo. Existence of extremal solutions for nonlinear fractional differential equation with nonlinear boundary conditions[J]. Applied Mathematics Letters, 2015, 41:46-51.
[6] NTOUYA S K, ETEMAD S. On the existence of solutions for fractional differential inclusions with sum and integral boundary conditions[J]. Applied Mathematics and Computation, 2015, 266:235-243.
[7] LÜ Zhiwei. Existence results for m-point boundary value problems of nonlinear fractional differential equations with p-Laplacian operator[J]. Advances in Difference Equations, 2014, 2014(1):1-16.
[8] LIU Xiping, JIA Mei, GE Weigao. Multiple solutions of a p-Laplacian model involving a fractional derivative[J]. Advances in Difference Equations, 2013, 2013(1):126.
[9] SUN Bo, GE Weigao. Existence and iteration of positive solutions to a class of Sturm-Liouville-like p-Laplacian boundary value problems[J]. Nonlinear Analysis: Theory, Methods & Applications, 2008, 69(4):1454-1461.
[10] CHEN Taiyong, LIU Wenbin, HU Zhigang. A boundary value problem for fractional differential equation with p-Laplacian operator at resonance[J]. Nonlinear Analysis: Theory, Methods & Applications, 2012, 75(6):3210-3217.
[11] CHEN Taiyong, LIU Wenbin. An anti-periodic boundary value problem for the fractional differential equation with a p-Laplacian operator[J]. Applied Mathematics Letters, 2012, 25:1671-1675.
[12] CHEN Yunmei, LEVINE S, RAO M. Variable exponent, linear growth functionals in image restoration[J]. SIAM journal on Applied Mathematics, 2006, 66(4):1383-1406.
[13] SZYMANEK E. The application of fractional order differential calculus for the description of temperature profiles in a granular layer[M]. Switzerland: Springer, 2013: 243-248.
[14] SHEN Tengfei, LIU Wenbin. Existence of solutions for fractional integral boundary value problems with p(t)-Laplacian operator[J]. Journal of Nonlinear Science and Applications, 2016, 9(2016):5000-5010.
[15] ZHANG Qihu, WANG Yan, QIU Zhimei. Existence of solutions and boundary asymptotic behavior of p(r)-Laplacian equation multi-point boundary value problems[J]. Nonlinear Analysis: Theory, Methods & Applications, 2010, 72(6):2950-2973.
[16] FAN Xianling, ZHANG Qihu, ZHAO Dun. Eigenvalues of p(x)-Laplacian Dirichlet problem[J]. Journal of Mathematical Analysis and Applications, 2005, 302(2):306-317.
[17] PODLUBNY I. Fractional differential equations [M]. San Diego: Academic Press,1999.
[18] MAWHIN J. Topological degree and boundary value problems for nonlinear differential equations[M]. Berlin: Springer, 1993: 74-142.
[1] 王素云,李永军. 带超越共振点非线性项的二阶常微分方程边值问题的可解性[J]. 山东大学学报（理学版）, 2018, 53(6): 53-56.
[2] 张申贵. 四阶变指数椭圆方程Navier边值问题的多解性[J]. 山东大学学报（理学版）, 2018, 53(2): 32-37.
[3] 闫东亮. 带有导数项的二阶周期问题正解[J]. 山东大学学报（理学版）, 2017, 52(9): 69-75.
[4] 张莎,贾梅,李燕,李晓晨. 分数阶脉冲微分方程三点边值问题解的存在性和唯一性[J]. 山东大学学报（理学版）, 2017, 52(2): 66-72.
[5] 崔玉军,赵聪. 四阶微分方程奇异边值问题解的唯一性[J]. 山东大学学报（理学版）, 2017, 52(2): 73-76.
[6] 冯海星,翟成波. 高阶非线性分数阶微分方程系统的多个正解[J]. 山东大学学报（理学版）, 2017, 52(12): 48-57.
[7] 苏小凤,贾梅,李萌萌. 共振条件下分数阶微分方程积分边值问题解的存在性[J]. 山东大学学报（理学版）, 2016, 51(8): 66-73.
[8] 仲秋艳,张兴秋. 含参数及p-Laplacian算子的奇异分数阶微分方程积分边值问题的正解[J]. 山东大学学报（理学版）, 2016, 51(6): 78-84.
[9] 江静,高庆龄,张克玉. 时标上二阶Dirichlet边值问题弱解的存在性[J]. 山东大学学报（理学版）, 2016, 51(6): 99-103.
[10] 朱雯雯. 一阶多点边值问题多个解的存在性[J]. 山东大学学报（理学版）, 2016, 51(6): 42-48.
[11] 陈彬,Abuelgasimalshaby Elzebir. 共振条件下的二阶多点边值问题解的存在性和多解性[J]. 山东大学学报（理学版）, 2016, 51(4): 49-52.
[12] 郭丽君. 非线性微分方程三阶三点边值问题正解的存在性[J]. 山东大学学报（理学版）, 2016, 51(12): 47-53.
[13] 张申贵. 带p(x)-调和算子的Kirchhoff型方程的多重解[J]. 山东大学学报（理学版）, 2016, 51(10): 48-53.
[14] 徐嫚. 奇异φ-Laplacian周期边值问题解的存在性[J]. 山东大学学报（理学版）, 2015, 50(08): 72-77.
[15] 马燕, 张克玉. 分数阶微分方程边值问题非平凡解的存在性[J]. 山东大学学报（理学版）, 2015, 50(05): 68-73.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
版权所有 © 2018 《山东大学学报(理学版)》编辑部　
地址: 山东省济南市山大南路27号山东大学中心校区（250100）　电话: +86-0531-88366917　E-mail: xblxb@sdu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发