MULTIPLICITY RESULTS FOR FOURTH ORDER ELLIPTIC EQUATIONS OF KIRCHHOFF-TYPE

doi:10.1016/S0252-9602(15)30040-0

数学物理学报(英文版) ›› 2015, Vol. 35 ›› Issue (5): 1067-1076.doi: 10.1016/S0252-9602(15)30040-0

MULTIPLICITY RESULTS FOR FOURTH ORDER ELLIPTIC EQUATIONS OF KIRCHHOFF-TYPE

许丽萍¹, 陈海波²

1. Department of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471003, China;
2. School of Mathematics and Statistics, Central South University, Changsha 410075, China

收稿日期:2014-01-17 修回日期:2015-05-07 出版日期:2015-09-01 发布日期:2015-09-01
通讯作者: Haibo CHEN E-mail:math_chb@csu.edu.cn
作者简介:Liping XU, E-mail: x.liping@126.com; Haibo CHEN, E-mail: math_chb@csu.edu.cn
基金资助:
This work was supported by Natural Science Foundation of China (11271372) and Hunan Provincial Natural Science Foundation of China (12JJ2004).

MULTIPLICITY RESULTS FOR FOURTH ORDER ELLIPTIC EQUATIONS OF KIRCHHOFF-TYPE

Liping XU¹, Haibo CHEN²

1. Department of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471003, China;
2. School of Mathematics and Statistics, Central South University, Changsha 410075, China

Received:2014-01-17 Revised:2015-05-07 Online:2015-09-01 Published:2015-09-01
Contact: Haibo CHEN E-mail:math_chb@csu.edu.cn
Supported by:
This work was supported by Natural Science Foundation of China (11271372) and Hunan Provincial Natural Science Foundation of China (12JJ2004).

摘要/Abstract

摘要：

In this paper, we concern with the following fourth order elliptic equations of Kirchhoff type
???11???
where a,b>0 are constants and the primitive of the nonlinearity f is of superlinear growth near infinity in u and is also allowed to be sign-changing. By using variational methods, we establish the existence and multiplicity of solutions. Our conditions weaken the Ambrosetti-Rabinowitz type condition.

关键词: fourth order elliptic equations of Kirchhoff type, symmetric mountain pass theorem, variational methods

Abstract:

Key words: fourth order elliptic equations of Kirchhoff type, symmetric mountain pass theorem, variational methods

中图分类号:

35J20

许丽萍, 陈海波. MULTIPLICITY RESULTS FOR FOURTH ORDER ELLIPTIC EQUATIONS OF KIRCHHOFF-TYPE[J]. 数学物理学报(英文版), 2015, 35(5): 1067-1076.

Liping XU, Haibo CHEN. MULTIPLICITY RESULTS FOR FOURTH ORDER ELLIPTIC EQUATIONS OF KIRCHHOFF-TYPE[J]. Acta mathematica scientia,Series B, 2015, 35(5): 1067-1076.

参考文献

[1] Ball J M. Initial-boundary value for an extensible beam. J Math Anal Appl, 1973, 42:61-90
[2] Berger H M. A new approach to the analysis of large deflections of plates. J Appl Mech, 1955, 22:465-472
[3] Ma T F. Positive solutions for a nonlocal fourth order equation of Kirchhoff type. Discrete Contin Dyn Syst, 2007, (Supplement):694-703
[4] Ma T F. Existence results for a model of nonlinear beam on elastic bearings. Appl Math Lett, 2000, 13:11-15
[5] Ma T F. Existence results and numerical solutions for a beam equation with nonlinear boundary conditions. Appl Numer Math, 2003, 47:189-196
[6] Wang F l, An Y K. Existence and multiplicity of solutions for a fourth-order elliptic equation. Bound Value Probl, 2012:6
[7] Wang F l, Avci M, An Y K. Existence of solutions for fourth order elliptic equations of Kirchhoff type. J Math Anal Appl, 2014, 409:140-146
[8] Xu L P, Chen H B. Existence and multiplicity of solutions for fourth-order elliptic equations of Kirchhoff type via genus theory. Boundary Value Problems 2014, 2014:212
[9] Wu Y Z, Huang Y S, Liu Z. Sign-changing solutions for Schrödunger equations with vanishing and signchanging potentials. Acta Mathematica Scientia, 2014, 34B(3):691-702
[10] Kang D S, Luo J, Shi X L. Solutions to elliptic systems involving doubly critical nonlinearities and Hardtype potentials. Acta Mathematica Scientia, 2015, 35B(2):423-438
[11] Zou W M, Schechter M. Critical Point Theory and its Applications. New York:Springer, 2006
[12] Willem M. Minimax Theorem. Boston, MA:Birkhäuser Boston Inc, 1996
[13] Rabinowitz P H. Minimax Methods in Critical Point Theory with Application to Differential Equations. CBMS Reg Conf Ser Math, Vol 65. Providence, RI:American Mathematical Society, 1986
[14] Zou W M. Variant fountain theorems and their applications. Manuscripta Math, 2001, 104:343-358

MULTIPLICITY RESULTS FOR FOURTH ORDER ELLIPTIC EQUATIONS OF KIRCHHOFF-TYPE

MULTIPLICITY RESULTS FOR FOURTH ORDER ELLIPTIC EQUATIONS OF KIRCHHOFF-TYPE

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 7

Metrics

本文评价

推荐阅读 10

[1]	贾慧芳, 李工宝. MULTIPLICITY AND CONCENTRATION BEHAVIOUR OF POSITIVE SOLUTIONS FOR SCHRÖDINGER-KIRCHHOFF TYPE EQUATIONS INVOLVING THE p-LAPLACIAN IN R^N[J]. 数学物理学报(英文版), 2018, 38(2): 391-418.
[2]	李全清, 吴鲜. EXISTENCE OF NONTRIVIAL SOLUTIONS FOR GENERALIZED QUASILINEAR SCHRÖDINGER EQUATIONS WITH CRITICAL OR SUPERCRITICAL GROWTHS[J]. 数学物理学报(英文版), 2017, 37(6): 1870-1880.
[3]	张金国, 刘晓春. THREE SOLUTIONS FOR A FRACTIONAL ELLIPTIC PROBLEMS WITH CRITICAL AND SUPERCRITICAL GROWTH[J]. 数学物理学报(英文版), 2016, 36(6): 1819-1831.
[4]	尚月赟, 王莉. MULTIPLE NONTRIVIAL SOLUTIONS FOR A CLASS OF SEMILINEAR POLYHARMONIC EQUATIONS[J]. 数学物理学报(英文版), 2014, 34(5): 1495-1509.
[5]	吴元泽, 黄毅生, 刘增. SIGN-CHANGING SOLUTIONS FOR SCHRÖDINGER EQUATIONS WITH VANISHING AND SIGN-CHANGING POTENTIALS[J]. 数学物理学报(英文版), 2014, 34(3): 691-702.
[6]	王影, 罗党, 王明新. POSITIVE SOLUTIONS TO THE p-LAPLACIAN WITH SINGULAR WEIGHTS[J]. 数学物理学报(英文版), 2012, 32(3): 1002-1020.
[7]	万优艳. MULTIPLE SOLUTIONS AND THEIR LIMITING BEHAVIOR OF COUPLED NONLINEAR SCHRÖDINGER SYSTEMS[J]. 数学物理学报(英文版), 2010, 30(4): 1199-1218.