Have a personal or library account? Click to login
Infinitely Many Solutions of the Neumann Problem for Elliptic systems in Anisotropic Variable Exponent Sobolev Spaces Cover

Infinitely Many Solutions of the Neumann Problem for Elliptic systems in Anisotropic Variable Exponent Sobolev Spaces

Open Access
|Aug 2017

References

  1. [1] A. Ahmed, T.Ahmedatt, H. Hjiaj and A. Touzani, Existence of infinitly many weak solu- tions for some quasilinear ~p(·)-elliptic Neumann problems, Mathematica Bohemica DOI: 10.21136/MB.2017.0037-15.10.21136/MB.2017.0037-15
  2. [2] A. Ahmed, H. Hjiaj and A. Touzani, Existence of infinitely many weak solutions for a Neumann elliptic equations involving the ~p(x)-laplacian operator, Rend. Circ. Mat. Palermo DOI 10.1007/s12215-015-0210-1.
  3. [3] A. Bechah, Local and global estimates for solutions of systems involving the p-Laplacian in unbounded domains, Electronic Journal of diffeerential equations, 19 (2001), pp. 1-14.
  4. [4] M. Bendahmane, M. Chrif and S. El Manouni, An Approximation Result in Generalized Anisotropic Sobolev Spaces and Application, Z. Anal. Anwend., 30 (2011), no. 3, 341-353.
  5. [5] M. Bendahmane, F. Mokhtari, Nonlinear elliptic systems with variable exponents and mea- sure data, Moroccan J. Pure and Appl. Anal.(MJPAA) Volume 1(2), 2015, Pages 108-125.10.7603/s40956-015-0008-3
  6. [6] A. Bensedik, M. Bouchekif, On certain nonlinear elliptic systems with indefinite terms, Electronic Journal of differential equations, 83 (2002), pp. 1-16.
  7. [7] L. Boccardo, D. Guedes De Figueiredo, Some Remarks on a system of quasilinear elliptic equations, Nonlinear differ. equ. appl., 9 (2002), pp. 309-323.
  8. [8] M. M. Boureanu, Infinitely many solutions for a class of degenerate anisotropic elliptic problems with variable exponent, Taiwanese J. Math. 15 (2011) 2291-2310.10.11650/twjm/1500406435
  9. [9] M. M. Boureanu, V.D. Radulescu, Anisotropic Neumann problems in Sobolev spaces with variable exponent, Nonlinear Analysis (2011), doi:10.1016/j.na.2011.09.033.
  10. [10] M. M. Boureanu, C. Udrea and D. N. Udrea, Anisotropic problems with variable exponents and constant Dirichlet condition, Electron. J. Diff. Equ., 2013 (2013), 1-13.10.1186/1687-1847-2013-1
  11. [11] X. L. Fan, D. Zhao, On the generalised Orlicz-Sobolev Space Wk;p(x)(), J. Gansu Educ. College12(1)(1998) 1-6.
  12. [12] B. Kone, S. Ouaro, S. Traore, Weak solutions for anisotropic nonlinear elliptic equations with variable exponents, Electron. J. Differential Equations 2009 (144) (2009) 1-11.
  13. [13] M. Mihăilescu, G. Morosanu, Existence and multiplicity of solutions for an anisotropic elliptic problem involving variable exponent growth conditions, Appl. Anal. 89 (2010) 257-271.10.1080/00036810802713826
  14. [14] D. S. Moschetto, Infintly many solutions to the Dirichlet problem for quasilinear elliptic systems involving the p(x) and q(x) Laplacien, Le matematiche Vol . LXIII (2008)Fasc. I, pp. 223-233.
  15. [15] D. S. Moschetto, Infinitely Many Solutions to the Neumann Problem for Quasilinear El- liptic Systems Involving the p(x) and q(x)-Laplacian, International Mathematical Forum, 4, 2009, no. 24, 1201-1211.
  16. [16] B. Ricceri, A general variational principle and some of its applications, J. Comput. Appl.Math. 113 (2000) 401-410.10.1016/S0377-0427(99)00269-1
  17. [17] D. Terman, Radial solutions of an elliptic system: solutions with a prescribed winding number, Houston Journal of mathematics, 15 (3) (1989).
  18. [18] J. Vélin, Existence result for a gradient-type elliptic system involving a pair of p(x) and q(x)-Laplacian operators, Complex Variables and Elliptic Equations, 2015, http://dx.doi.org/10.1080/17476933.2015.111057810.1080/17476933.2015.1110578
  19. [19] L. Zhao, P. Zhao, X. Xie, Existence and multiplicity of solutions for divergence type elliptic equations, Electronic Journal of Differential Equations 2011 (2011) no. 43, 1-9.
  20. [20] W. Zou,S. Li, J. Q. Liu, Nontrivial solutions for resonant cooperative elliptic systems via computations of critical groups, Nonlinear Analysis, 38(1999) pp. 229-247.
Language: English
Page range: 70 - 82
Published on: Aug 1, 2017
Published by: Sciendo
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year

© 2017 A. Ahmed, M.S.B. Elemine Vall, A. Touzani, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.