Have a personal or library account? Click to login
A Generalized Version of the Lions-Type Lemma Cover
Open Access
|Aug 2023

References

  1. R.A. Adams and J.J.F. Fournier, Sobolev Spaces, second edition, Pure Appl. Math. (Amst.), 140, Elsevier/Academic Press, Amsterdam, 2003.
  2. C.O. Alves and M.L.M. Carvalho, A Lions type result for a large class of Orlicz-Sobolev space and applications, Mosc. Math. J. 22 (2022), no. 3, 401–426.
  3. C.O. Alves, G.M. Figueiredo, and J.A. Santos, Strauss and Lions type results for a class of Orlicz-Sobolev spaces and applications, Topol. Methods Nonlinear Anal. 44 (2014), no. 2, 435–456.
  4. S. Bahrouni, H. Ounaies, and O. Elfalah, Problems involving the fractional g-Laplacian with lack of compactness, J. Math. Phys. 64 (2023), no. 1, Paper No. 011512, 18 pp.
  5. G. Barletta and A. Cianchi, Dirichlet problems for fully anisotropic elliptic equations, Proc. Roy. Soc. Edinburgh Sect. A 147 (2017), no.1, 25–60.
  6. Ph. Clément, M. García-Huidobro, R. Manásevich, and K. Schmitt, Mountain pass type solutions for quasilinear elliptic equations, Calc. Var. Partial Differential Equations 11 (2000), no. 1, 33–62.
  7. D.G. Costa, An Invitation to Variational Methods in Differential Equations, Birkhäuser Boston, Inc., Boston, MA, 2007.
  8. M. Lewin, Describing lack of compactness in Sobolev spaces, lecture notes on Variational Methods in Quantum Mechanics, University of Cergy-Pontoise, 2010. Avaliable at HAL: hal-02450559.
  9. E.H. Lieb, On the lowest eigenvalue of the Laplacian for the intersection of two domains, Invent. Math. 74 (1983), no. 3, 441–448.
  10. P.L. Lions, The concentration-compactness principle in the calculus of variations. The locally compact case. I, Ann. Inst. H. Poincaré Anal. Non Linéaire 1 (1984), no. 2, 109–145.
  11. E.D. Silva, M.L. Carvalho, J.C. de Albuquerque, and S. Bahrouni, Compact embedding theorems and a Lions’ type lemma for fractional Orlicz-Sobolev spaces, J. Differential Equations 300 (2021), 487–512.
  12. M. Struwe, Variational Methods, fourth edition, Ergeb. Math. Grenzgeb. (3), 34 [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], Springer–Verlag, Berlin, 2008.
  13. K. Wroński, Quasilinear elliptic problem in anisotrpic Orlicz-Sobolev space on unbounded domain, arXiv preprint, 2022. Avaliable at arXiv: 2209.10999.
DOI: https://doi.org/10.2478/amsil-2023-0014 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107
Language: English
Page range: 240 - 247
Submitted on: Feb 2, 2023
Accepted on: Aug 1, 2023
Published on: Aug 28, 2023
Published by: University of Silesia in Katowice, Institute of Mathematics
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2023 Magdalena Chmara, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution 4.0 License.