Have a personal or library account? Click to login

Infinitely many solutions for a class of hemivariational inequalities involving p(x)-Laplacian

Open Access
|Sep 2017

References

  1. [1] M. Alimohammady, F. Fattahi, Existence of solutions to hemivaritional inequalities involving the p(x)-biharmonic operator, Electron. J. Diff. Equ., 2015(2015), no. 79, 1-12.
  2. [2] M. Allaoui, Existence of solutions for a Robin problem involving the p(x)-Laplacian, Applied Mathematics E-Notes, 14(2014), 107-115.
  3. [3] A. Ambrosetti, A. Malchiodi, Nonlinear Analysis and Semilinear Elliptic Problems, Cambridge Studies in Advanced Mathematics 104. Cambridge: Cambridge University Press, 2007.10.1017/CBO9780511618260
  4. [4] G. Bonannoa, D. Motreanu, P. Winkert, Variational-hemivariational inequalities with small perturbations of nonhomogeneous Neumann boundary conditions, J. Math. Anal. Appl. 381(2011), 627-637.10.1016/j.jmaa.2011.03.015
  5. [5] G. Bonannoa, P. Winkert, Multiplicity results to a class of variationalhemivariational inequalities, Topological methods in nonlinear analysis, 43(2)(2014), 493-516.10.12775/TMNA.2014.029
  6. [6] F. H. Clarke, Optimization and nonsmooth analysis, John Wiley & Sons, New York, 1983.
  7. [7] G. D'AGUÌ, Second-order boundary-value problems with variable exponents, Electronic Journal of differential Equations, 2014(2014), no. 68, 1-10.
  8. [8] S. G. Dend, Eigenvalues of the p(x)-laplacian Steklov problem, J. Math. Anal. Appl., 339 (2008), 925-937.10.1016/j.jmaa.2007.07.028
  9. [9] L. Diening, Riesz potential and Sobolev embeddings on generalized Lebesgue and Sobolev spaces Lp(x)() and W1;p(x)(), Math. Nachr. 268(2004), 31-43.10.1002/mana.200310157
  10. [10] D. E. Edmunds, J. Rákosník, Density of smooth functions in Wk;p(x)(); Proc. R. Soc. A, 437(1992), 229-236.10.1098/rspa.1992.0059
  11. [11] X. L. Fan, D. Zhao, On the generalized Orlicz - Sobolev space Wm;p(x)(); J. Gansu Educ. College, 12(1998), 1-6.
  12. [12] S. Heidarkhani, G. Afrouzi, A. Hadjian, J. henderson, Existence of infinitely many anti-periodic solutions for second-order impulsive differential inclusions, Electronic Journal of differential Equations, 2013(2013), no. 97, 1-13.
  13. [13] A. Kristály, Infinitely many radial non-radial solutions for a class of hemivariational inequalities, Rocky Mountain Journal of Mathematics, Vol. 35, 4(2005), 1173-1190.10.1216/rmjm/1181069682
  14. [14] R. Kajikiya, A critical-point theorem related to the symmetric mountain-pass lemma and its applications to elliptic equations, J. Funct. Analysis, 225(2005), 352-370.10.1016/j.jfa.2005.04.005
  15. [15] L. Li, C. Tang, Existence and multiplicity of solutions for a class of p(x)-biharmonic equations, Acta Mathematica Scientia, 33B(1)(2013), 155-170.10.1016/S0252-9602(12)60202-1
  16. [16] G. Sun, K. Teng, Existence and multiplicity of solutions for a class of fractional Kirchhoff-type problem, Math. Commun. 183 19(2014), 183-194.
  17. [17] M. C. Wei, C. L. Tang, Existence and Multiplicity of Solutions for p(x)-Kirchhoff-Type Problem in RN, Bull. Malays. Math. Sci. Soc. (2) 36(3)(2013), 767-781.
  18. [18] Y. Ye, C.L. Tang, Multiplicity of solutions for elliptic boundary value problems, Electronic Journal of differential Equations, 2014(2014), No. 140, 1-13.10.1186/1687-2770-2014-105
  19. [19] X. L. Fan, Regularity of minimizers of variational integrals with p(x)-growth conditions, Ann. Math. Sinica, 17A(5)(1996), 557-564.
  20. [20] O. Kováčik , J. Rákosnínk , On spaces Lp(x) and W1;p(x); Czechoslovak Math. J., 41(1991), 592-618.10.21136/CMJ.1991.102493
  21. [21] X. L. Fan, Q. H. Zhang, Existence of solutions for p(x)-Laplacian Dirichlet problems , Nonlinear Anal., 52(2003), 1843-1852.10.1016/S0362-546X(02)00150-5
  22. [22] L. Li, L. Ding, W. W. Pan, Existence of multiple solutions for a p(x)-biharmonic equation, Electron J Differ Equ, 2013(2013), No. 139, 1-10.10.1186/1687-1847-2013-260
  23. [23] D. Motreanu, P. Winkert, Variational-hemivariational inequalities with nonhomogeneous neumann boundary condition, Le Matematiche, Vol. (2010) Fasc. II, 109-119 doi: 10.4418/2010.65.2.12
  24. [24] V. Rădulescu, Nonlinear elliptic equations with variable exponent: old and new, Nonlinear Analysis, Theory, Methods and Applications, 121(2015), 336-369.10.1016/j.na.2014.11.007
  25. [25] V. Rădulescu, D. Repovs, Partial differential equations with variable exponents, Variational Methods and Qualitative Analysis, CRC Press, Taylor & Francis Group, Boca Raton, 2015.10.1201/b18601
DOI: https://doi.org/10.1515/auom-2017-0021 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784
Language: English
Page range: 65 - 83
Submitted on: Jul 7, 2016
Accepted on: Sep 19, 2016
Published on: Sep 21, 2017
Published by: Ovidius University of Constanta
In partnership with: Paradigm Publishing Services
Publication frequency: 3 times per year

© 2017 Fariba Fattahi, Mohsen Alimohammady, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.