A Generalized Version of the Lions-Type Lemma

[1] R.A. Adams and J.J.F. Fournier, Sobolev Spaces, second edition, Pure Appl. Math. (Amst.), 140, Elsevier/Academic Press, Amsterdam, 2003.Search in Google Scholar

[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.Search in Google Scholar

[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.Search in Google Scholar

[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.Search in Google Scholar

[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.Search in Google Scholar

[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.Search in Google Scholar

[7] D.G. Costa, An Invitation to Variational Methods in Differential Equations, Birkhäuser Boston, Inc., Boston, MA, 2007.Search in Google Scholar

[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.Search in Google Scholar

[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.Search in Google Scholar

[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.Search in Google Scholar

[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.Search in Google Scholar

[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.Search in Google Scholar

[13] K. Wroński, Quasilinear elliptic problem in anisotrpic Orlicz-Sobolev space on unbounded domain, arXiv preprint, 2022. Avaliable at arXiv: 2209.10999.Search in Google Scholar