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） ›› 2016, Vol. 51 ›› Issue (10): 48-53.doi: 10.6040/j.issn.1671-9352.0.2015.309

• • 上一篇    下一篇

带p(x)-调和算子的Kirchhoff型方程的多重解

张申贵   

  1. 西北民族大学数学与计算机科学学院, 甘肃 兰州 730030
  • 收稿日期:2015-06-29 出版日期:2016-10-20 发布日期:2016-10-17
  • 作者简介:张申贵(1980— ), 男, 博士, 副教授, 研究方向为非线性泛函分析和偏微分分方程. E-mail:zhangshengui315@163.com
  • 基金资助:
    国家自然科学基金资助项目(31260098);天元数学基金资助项目(11326100);西北民族大学中央高校基本科研业务费专项资助(31920130004)

Multiplicity of solutions for Kirchhoff type equation involving the p(x)-biharnonic operator

ZHANG Shen-gui   

  1. College of Mathematics and Computer Science, Northwest University for Nationalities, Lanzhou 730030, Gansu, China
  • Received:2015-06-29 Online:2016-10-20 Published:2016-10-17

PDF (PC)

743

摘要： 研究了一类Kirchhoff型p(x)-调和方程。利用临界点理论中的喷泉定理,获得了多重解存在的充分条件,推广和改进了一些已有的结果。

关键词: p(x)-调和算子, Navier边值问题, Kirchhoff型方程, 临界点

Abstract: A class of Kirchhoff type equation involving the p(x)-biharnonic operator is ivestigated. By using fountain theorem in critical point theory, some sufficient conditions for the existence of multiplicity of solutions are obtained, which generalize and improve some existing resuls.

Key words: p(x)-biharnonic operator, Navier boundary value problem, Kirchhoff type equation, critical point

中图分类号: 

  • O175.8
[1] ZHIKOV V. On some variational problems[J]. Russian J Math Phys, 1997, 5:105-116.
[2] RUZICKA M. Electrorheologial fluids: modeling and mathematial throry[M]. Berlin: Springer-Verlag, 2000.
[3] CHEN Y, LEVINE S, RAO M. Variable exponent, linear growth functionals in image restoration[J]. SIAM J Appl Math, 2006, 66, 4:1383-1406.
[4] LIN Lin, TANG Chunlei. Existence and multiplicity of solutions for a class of p(x)-biharmonic equations[J]. Acta Mathematica Scientia, 2013, 33(1):155-170.
[5] YIN Honghui, YANG Zuodong. Three solutions for a navier boundary value system involving the(p(x), q(x))-biharmonic operator[J]. British Journal of Mathematics Computer Science, 2013, 3(3):281-290.
[6] YIN, Honghui, LIU Ying. Existence of three solutions for a Navier boundary value problem involving the p(x)-biharnonic operator[J]. Bull. Korean Math Soc, 2013, 50(6):1817-1826.
[7] AFROUZI G A, MIRZAPOUR M, RADULESCU V D. Nonlocal fourth-order Kirchhoff systems with variable growth: low and high energy solutions[J]. Collectanea Mathematica, 2015, 5:1-17.
[8] KONG Lingju. Eigenvalues for a fourth order elliptic problem[J]. Proceedings of the American Mathematical Society, 2015, 143(1):249-258.
[9] 张申贵. 一类超线性p(x)-调和方程的无穷多解[J]. 山东大学学报(理学版), 2012, 47(10):116-120. ZHANG Shengui. Infinitely many solutions for a class of superlinear p(x)-biharmonic equation[J]. Journal of Shandong University(Natural Science), 2012, 47(10):116-120.
[10] AMROUSS A E, MORADI F, MOUSSOUI M. Existence of solutions for fourth-order PDES with variable exponents[J]. Electron J Differential Equations, 2009, 153:1-13.
[11] WILLEM M. Minimax theorems[M]. Boston: Birkhauser, 1996.
[12] DING Yanheng, LUAN Shixia. Multiple solutions for a class of nonlinear Schr(¨overo)dinger equations[J]. J Differential Equations, 2004, 207:423-457.
[1] 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.
[2] 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.
[3] 孙国伟, 买阿丽. 一类二阶非线性差分方程同宿解的多解性[J]. 山东大学学报（理学版）, 2015, 50(05): 51-54.
[4] 张申贵. 局部超线性p-基尔霍夫方程的多重解[J]. 山东大学学报（理学版）, 2014, 49(05): 61-68.
[5] 张国威1,陈昂2. 初始例函数的游荡域的无穷连通性[J]. 山东大学学报（理学版）, 2014, 49(04): 70-73.
[6] 张申贵. 一类超线性p(x)-调和方程的无穷多解[J]. J4, 2012, 47(10): 116-120.
[7] 张申贵. 一类非自治二阶系统的多重周期解[J]. J4, 2011, 46(11): 64-69.
[8] 朱海霞1,晏世雷2. 随机晶场作用的Blume-Capel模型的相图研究[J]. J4, 2011, 46(1): 51-55.
[9] 许万银. 一类拟线性Neumann问题的多重解[J]. J4, 2009, 44(10): 39-42.
[10] 张懿彬 . 带指数增长型Neumann边界条件的Laplace方程解的存在性[J]. J4, 2008, 43(3): 48-53 .
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