Research Article
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Year 2022, , 112 - 130, 30.06.2022
https://doi.org/10.53006/rna.1021871

Abstract

References

  • [1] R.A. Adams, J.F. Fournier, Sobolev spaces, Second edition, Pure and Applied Mathematics (Amsterdam), Elsevier/Academic Press, Amsterdam, (2003).
  • [2] K. Adriouch, A. El Hamidi, The Nehari manifold for systems of nonlinear elliptic equations. Nonlinear Analysis: Theory, Methods Applications, 64(10), (2006), 2149-2167.
  • [3] G.A. Afrouzi, S. Heidarkhani, Existence of three solutions for a class of Dirichlet quasilinear ellip- tic systems involving the (p1,, pn)-Laplacian. Nonlinear Analysis: Theory, Methods Applications, 70(1) (2009), 135-143.
  • [4] K.B. Ali, M. Hsini, K. Kefi, N.T. Chung, On a nonlocal fractional p (.,.)-Laplacian problem with competing nonlinearities. Complex Analysis and Operator Theory, 13(3) (2019), 1377-1399.
  • [5] E. Azroul, A. Benkirane, & M. Srati, Nonlocal eigenvalue type problem in fractional Orlicz- Sobolev space. Advances in Operator Theory, 5(4) (2020), 1599-1617.
  • [6] E. Azroul, A. Benkirane, M. Srati, & M. Shimi, Existence of solutions for a nonlocal Kirchhoff type problem in Fractional Orlicz-Sobolev spaces. arXiv preprint arXiv:1901.05216, (2019).
  • [7] E. Azroul, A. Benkirane, M. Srati, Existence of solutions for a non-local type problem in Frac- tional Orlicz Sobolev Spaces, Adv. Oper. Theory (2020).
  • [8] E. Azroul, A. Benkirane, M. Srati, Mountain pass type solution for a nonlacal fractional a- Kirchhoff type problem J. Nonlinear Funct. Anal. 2020 (2020), Article ID 22.
  • [9] E. Azroul, A. Boumazourh, On a class of fractional systems with nonstandard growth conditions, J. PseudoDiffer. Oper. Appl. 11 (2020), 805-820.
  • [10] S. Bahrouni, H. Ounaies, L.S. Tavares, Basic results of fractional Orlicz-Sobolev space and applications to non-local problems, (2019).
  • [11] A. Boumazourh and M. Srati, Leray-Schauder’s solution for a nonlocal problem in a fractional Orlicz-Sobolev space. Moroccan J. of Pure and Appl. Anal. (MJPAA) doi : 10.2478/mjpaa-2020-0004 (2020) 42-52.
  • [12] J.F. Bonder, and A.M. Salort, Fractional order Orlicz-Sobolev Spaces, Journal of Functional Analysis, 2019, https://doi.org/10.1016/j.jfa.2019.04.003.
  • [13] L. Boccardo, D. Guedes de Figueiredo, Some remarks on a system of quasilinear elliptic equa- tions, NoDEA Nonlinear Differential Equations Appl., 9 (2002), 309-323.
  • [14] F.J.S.A. Corrˆ ea, M.L.M. Carvalho, Jose VA Goncalves, et al., Positive solutions of strongly nonlinear elliptic problems. Asymptotic Analysis, 2015, vol. 93, no 1-2, p. 1-20.
  • [15] F.J.S.A. Corrˆ ea, M.L.M. Carvalho, Jose VA Goncalves, et al., Sign changing solutions for quasi- linear superlinear elliptic problems. Quarterly Journal of Mathematics, 2017, vol. 68, no 2, p. 391-420.
  • [16] Y. Chen, S. Levine, M. Rao, Variable exponent linear growth functionals in image processing, SIAM J. Appl. Math., 66 (2006), 1383-1406.
  • [17] L. Diening, Theorical and numerical results for electrorheological fluids, Ph.D. thesis, University of Freiburg, Germany (2002)
  • [18] N. Fukagai, M. Ito, K. Narukawa, Positive solutions of quasilinear elliptic equations with critical Orlicz-Sobolev nonlinearity on RN, Funkcial. Ekvac., 49 (2006), 235-267.
  • [19] T.C. Halsey, Electrorheological fluids, Science, 258 (1992), 761-766. https://doi.org/10.1016/j.jfa.2019.04.003.
  • [20] El-houari Hamza, L.S. Chadli, and H. Moussa, Existence of Solution To M-Kirchhoff System Type, 2021 7th International Conference on Optimization and Applications (ICOA). IEEE, 2021.
  • [21] M.A. Krasnosel’skii, Y.B. Rutickii, Convex functions and Orlicz spaces (Vol. 9) (1961), Gronin- gen: Noordhoff.

Existence of ground state solutions of elliptic system in Fractional Orlicz-Sobolev Spaces

Year 2022, , 112 - 130, 30.06.2022
https://doi.org/10.53006/rna.1021871

Abstract

We employing a minimization arguments on appropriate Nehari manifolds, we obtain ground state solutions
for a non-local elliptic system driven by the fractional a(.)-Laplacian operator, with Dirichlet boundary
conditions type.

References

  • [1] R.A. Adams, J.F. Fournier, Sobolev spaces, Second edition, Pure and Applied Mathematics (Amsterdam), Elsevier/Academic Press, Amsterdam, (2003).
  • [2] K. Adriouch, A. El Hamidi, The Nehari manifold for systems of nonlinear elliptic equations. Nonlinear Analysis: Theory, Methods Applications, 64(10), (2006), 2149-2167.
  • [3] G.A. Afrouzi, S. Heidarkhani, Existence of three solutions for a class of Dirichlet quasilinear ellip- tic systems involving the (p1,, pn)-Laplacian. Nonlinear Analysis: Theory, Methods Applications, 70(1) (2009), 135-143.
  • [4] K.B. Ali, M. Hsini, K. Kefi, N.T. Chung, On a nonlocal fractional p (.,.)-Laplacian problem with competing nonlinearities. Complex Analysis and Operator Theory, 13(3) (2019), 1377-1399.
  • [5] E. Azroul, A. Benkirane, & M. Srati, Nonlocal eigenvalue type problem in fractional Orlicz- Sobolev space. Advances in Operator Theory, 5(4) (2020), 1599-1617.
  • [6] E. Azroul, A. Benkirane, M. Srati, & M. Shimi, Existence of solutions for a nonlocal Kirchhoff type problem in Fractional Orlicz-Sobolev spaces. arXiv preprint arXiv:1901.05216, (2019).
  • [7] E. Azroul, A. Benkirane, M. Srati, Existence of solutions for a non-local type problem in Frac- tional Orlicz Sobolev Spaces, Adv. Oper. Theory (2020).
  • [8] E. Azroul, A. Benkirane, M. Srati, Mountain pass type solution for a nonlacal fractional a- Kirchhoff type problem J. Nonlinear Funct. Anal. 2020 (2020), Article ID 22.
  • [9] E. Azroul, A. Boumazourh, On a class of fractional systems with nonstandard growth conditions, J. PseudoDiffer. Oper. Appl. 11 (2020), 805-820.
  • [10] S. Bahrouni, H. Ounaies, L.S. Tavares, Basic results of fractional Orlicz-Sobolev space and applications to non-local problems, (2019).
  • [11] A. Boumazourh and M. Srati, Leray-Schauder’s solution for a nonlocal problem in a fractional Orlicz-Sobolev space. Moroccan J. of Pure and Appl. Anal. (MJPAA) doi : 10.2478/mjpaa-2020-0004 (2020) 42-52.
  • [12] J.F. Bonder, and A.M. Salort, Fractional order Orlicz-Sobolev Spaces, Journal of Functional Analysis, 2019, https://doi.org/10.1016/j.jfa.2019.04.003.
  • [13] L. Boccardo, D. Guedes de Figueiredo, Some remarks on a system of quasilinear elliptic equa- tions, NoDEA Nonlinear Differential Equations Appl., 9 (2002), 309-323.
  • [14] F.J.S.A. Corrˆ ea, M.L.M. Carvalho, Jose VA Goncalves, et al., Positive solutions of strongly nonlinear elliptic problems. Asymptotic Analysis, 2015, vol. 93, no 1-2, p. 1-20.
  • [15] F.J.S.A. Corrˆ ea, M.L.M. Carvalho, Jose VA Goncalves, et al., Sign changing solutions for quasi- linear superlinear elliptic problems. Quarterly Journal of Mathematics, 2017, vol. 68, no 2, p. 391-420.
  • [16] Y. Chen, S. Levine, M. Rao, Variable exponent linear growth functionals in image processing, SIAM J. Appl. Math., 66 (2006), 1383-1406.
  • [17] L. Diening, Theorical and numerical results for electrorheological fluids, Ph.D. thesis, University of Freiburg, Germany (2002)
  • [18] N. Fukagai, M. Ito, K. Narukawa, Positive solutions of quasilinear elliptic equations with critical Orlicz-Sobolev nonlinearity on RN, Funkcial. Ekvac., 49 (2006), 235-267.
  • [19] T.C. Halsey, Electrorheological fluids, Science, 258 (1992), 761-766. https://doi.org/10.1016/j.jfa.2019.04.003.
  • [20] El-houari Hamza, L.S. Chadli, and H. Moussa, Existence of Solution To M-Kirchhoff System Type, 2021 7th International Conference on Optimization and Applications (ICOA). IEEE, 2021.
  • [21] M.A. Krasnosel’skii, Y.B. Rutickii, Convex functions and Orlicz spaces (Vol. 9) (1961), Gronin- gen: Noordhoff.
There are 21 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Hamza El-houari

Lalla Saadia Chadli 0000-0002-0659-8774

Hicham Moussa This is me

Publication Date June 30, 2022
Published in Issue Year 2022

Cite

APA El-houari, H., Chadli, L. S., & Moussa, H. (2022). Existence of ground state solutions of elliptic system in Fractional Orlicz-Sobolev Spaces. Results in Nonlinear Analysis, 5(2), 112-130. https://doi.org/10.53006/rna.1021871
AMA El-houari H, Chadli LS, Moussa H. Existence of ground state solutions of elliptic system in Fractional Orlicz-Sobolev Spaces. RNA. June 2022;5(2):112-130. doi:10.53006/rna.1021871
Chicago El-houari, Hamza, Lalla Saadia Chadli, and Hicham Moussa. “Existence of Ground State Solutions of Elliptic System in Fractional Orlicz-Sobolev Spaces”. Results in Nonlinear Analysis 5, no. 2 (June 2022): 112-30. https://doi.org/10.53006/rna.1021871.
EndNote El-houari H, Chadli LS, Moussa H (June 1, 2022) Existence of ground state solutions of elliptic system in Fractional Orlicz-Sobolev Spaces. Results in Nonlinear Analysis 5 2 112–130.
IEEE H. El-houari, L. S. Chadli, and H. Moussa, “Existence of ground state solutions of elliptic system in Fractional Orlicz-Sobolev Spaces”, RNA, vol. 5, no. 2, pp. 112–130, 2022, doi: 10.53006/rna.1021871.
ISNAD El-houari, Hamza et al. “Existence of Ground State Solutions of Elliptic System in Fractional Orlicz-Sobolev Spaces”. Results in Nonlinear Analysis 5/2 (June 2022), 112-130. https://doi.org/10.53006/rna.1021871.
JAMA El-houari H, Chadli LS, Moussa H. Existence of ground state solutions of elliptic system in Fractional Orlicz-Sobolev Spaces. RNA. 2022;5:112–130.
MLA El-houari, Hamza et al. “Existence of Ground State Solutions of Elliptic System in Fractional Orlicz-Sobolev Spaces”. Results in Nonlinear Analysis, vol. 5, no. 2, 2022, pp. 112-30, doi:10.53006/rna.1021871.
Vancouver El-houari H, Chadli LS, Moussa H. Existence of ground state solutions of elliptic system in Fractional Orlicz-Sobolev Spaces. RNA. 2022;5(2):112-30.