JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2018, Vol. 53 ›› Issue (2): 32-37.doi: 10.6040/j.issn.1671-9352.0.2017.359

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Multiple solutions of Navier boundary value problem for fourth-order elliptic equation with variable exponents

ZHANG Shen-gui   

  1. College of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, Gansu, China
  • Received:2017-07-19 Online:2018-02-20 Published:2018-01-31

Abstract: A class of Navier boundary value problem for fourth-order elliptic equation with variable exponents is investigated. When the nonlinear term is growing superlinearly, some sufficient conditions for the existence of multiplicity of solutions are obtained by using the fountain theorem in critical point theory.

Key words: critical point, Navier boundary value problem, fourth-order elliptic equation with variable exponents

CLC Number: 

  • 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 theory[M]. Berlin: Springer-Verlag, 2000.
[3] 黎芳, 刘瑞华. p(x)-调和映射在图像恢复中的应用[J].中国图象图形学报,2008,13(1):19-23. LI Fang, LIU Ruihua.The application of p(x)-Harmonic mapping in image processing[J]. Journal of Image and Graphics, 2008, 13(1):19-23.
[4] CHEN Y, LEVINE S, RAO M. Variable exponent, linear growth functionals in image restoration[J]. SIAM J Appl Math, 2006, 66(4):1383-1406.
[5] 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.
[6] 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.
[7] YE Yiwei, TANG Chunlei. Infinitely many solutions for fourth-order elliptic equations[J].J Math Anal Appl, 2012, 394(2):841-854.
[8] 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.
[9] KONG Lingju. Eigenvalues for a fourth order elliptic problem[J]. Proceedings of the American Mathematical Society, 2015, 143(1):249-258.
[10] HEIDARKHANI S, AFROUZI G A, MORADI S, et al. Existence of one weak solution for p(x)-biharmonic equations with Navier boundary conditions[J]. ZAngew Math Phys, 2016, 67(3):1-13.
[11] BARTSCH T. Infinitely many solutions of a symmetric Dirichlet problem[J]. Nonlinear Analysis, 1993, 20(10):1205-1216.
[12] MIYAGAKI O H, SOUTO M S. Superlinear problems without Ambrosetti and Rabinowitz growth condition[J]. Journal Differential Equations, 2008, 245(12):3628-3638.
[13] TANG Chunlei, WU Xingping. Periodic solutions for a class of new superquadratic second order Hamiltonian systems[J]. Appl Math Lett, 2014, 34(1):65-71.
[14] YE Yiwei. Infinitely many solutions for Kirchhoff type problems[J]. Differential Equations Applications, 2013, 5(1):83-92.
[15] 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. ZHANG Shengui. Multiplicity of solutions for Kirchhoff type equation involving the p(x)-biharnonic operator[J]. Journal of Shandong University(Natural Science), 2016, 51(10):48-53.
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