[
[1] A. Adimurthi, Existence results for the semilinear Dirichlet problem with critical growth for the n-Laplacian, Houst. J. Math. 7 (1991), 285-298.
]Search in Google Scholar

[
[2] Adimurthi and K. Sandeep, A Singular Moser-Trudinger Embedding and Its Applications, Nonlinear Differential Equations and Applications, 13 (2007), 585-603.10.1007/s00030-006-4025-9
]Search in Google Scholar

[
[3] S. Alama, Y. Y. Li, Existence of solutions for semilinear elliptic equations with indefinite linear part, J. Differential Equations 96 (1992), 89-115.10.1016/0022-0396(92)90145-D
]Search in Google Scholar

[
[4] C. O. Alves, L. R. de Freitas, Multiplicity of nonradial solutions for a class of quasilinear equations on annulus with exponential critical growth, Topol. Methods Nonlinear Anal. 39 (2012), 243-262.
]Search in Google Scholar

[
[5] C. O. Alves, J. M. do, O. H. Miyagaki, On nonlinear perturbations of a periodic elliptic problem in ℝ]^{2} involving critical growth, Nonlinear Anal. 56 (2004), 781-791.10.1016/j.na.2003.06.003
Search in Google Scholar

[
[6] A. Ambrosetti and P. H. Rabionowitz, Dual variational methods in critical points theory and applications, J. Funct. Anal. 14 (1973), 349-381.10.1016/0022-1236(73)90051-7
]Search in Google Scholar

[
[7] R. Aris, The Mathematical theory of Diffusion and reaction in permeable catalyst, Vol 1, Vol 2. Clarendon Press Oxford, 1975.
]Search in Google Scholar

[
[8] G. Astrita, G. Marrucci, Principles of Non-Newtonian Fluid Mechanics, McGraw-Hill New York, NY, USA, (1974).
]Search in Google Scholar

[
[9] L. Boccardo and F. Murat, Almost everywhere convergence of the gradients of solutions to elliptic and parabolic equations, Nonlinear Anal., 19 (1992), 581-597.10.1016/0362-546X(92)90023-8
]Search in Google Scholar

[
[10] E. Caglioti, P. L. Lions, C. Marchioro and M. Pulvirenti, A Special Class of Stationary Flows for Two-Dimensional Euler Equations: a Statistical Mechanics Description, Communications in Mathematical Physics, 143 (1992), 501-525.10.1007/BF02099262
]Search in Google Scholar

[
[11] E. Caglioti, P. L. Lions, C. Marchioro and M. Pulvirenti, A Special Class of Stationary Flows for Two-Dimensional Euler Equations: a Statistical Mechanics Description. II, Commun. Math. Phys., 174 (1995), 229-260.10.1007/BF02099602
]Search in Google Scholar

[
[12] M. Calanchi and B. Ruf, On Trudinger-Moser type inequalities with logarithmic weights, J. of Differential Equations 258 (2015), 1967-1989.10.1016/j.jde.2014.11.019
]Search in Google Scholar

[
[13] M. Calanchi and B. Ruf, Trudinger-Moser type inequalities with logarithmic weights in dimension N, Nonlinear Analysis, Series A; Theory Methods and Applications 121 (2015), 403-411.10.1016/j.na.2015.02.001
]Search in Google Scholar

[
[14] M. Calanchi and B. Ruf, Weighted Trudinger-Moser inequalities and Applications, Bulletin of the South Ural State University. Ser. Mathematical Modelling, programming and Computer Software 8 (2015), 42-55.
]Search in Google Scholar

[
[15] M. Calanchi, B. Ruf and F. Sani, Elliptic equations in dimension 2 with double exponential nonlinearities, NoDea Nonlinear Di er. Equ. Appl., 24 (2017), Art. 29.
]Search in Google Scholar

[
[16] M. Calanchi and E. Terraneo, Non-radial Maximizers For Functionals With Exponential Non- linearity in ℝ]^{2}, Advanced Nonlinear Studies 5 (2005), 337-350.10.1515/ans-2005-0302
Search in Google Scholar

[
[17] S. Chanillo and M. Kiessling, Rotational Symmetry of Solutions of Some Nonlinear Problems in Statistical Mechanics and in Geometry, Communications in Mathematical Physics, 160 (1994), 217-238.10.1007/BF02103274
]Search in Google Scholar

[
[18] S. Deng, T. Hu and C.Tang, N-laplacian problems with critical double exponential nonlinearities, DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 41 (2021), 987-1003.10.3934/dcds.2020306
]Search in Google Scholar

[
[19] W. Y. Ding, W. M. Ni, On the existence of positive entire solutions of a semilinear elliptic equation, Arch. Ration. Math. Anal. 31 (1986), 283-308.10.1007/BF00282336
]Search in Google Scholar

[
[20] P. Drabek, A. Kufner and F. Nicolosi, Quasilinear Elliptic Equations with Degenerations and Singularities, Walter de Gruyter, Berlin 1997.10.1515/9783110804775
]Search in Google Scholar

[
[21] X. Fang, J. Zhang, Multiplicity of positive solutions for quasilinear elliptic equations involving critical nonlinearity, Adv. Nonlinear Anal. 9 (2020), no. 1, 1420-1436.
]Search in Google Scholar

[
[22] D. G. de Figueiredo, J. M. do, B. Ruf, On an inequality by N. Trudinger and J. Moser and related elliptic equations, Comm. Pure Appl. Math. LV (2002), 135-152.10.1002/cpa.10015
]Search in Google Scholar

[
[23] D. G. de Figueiredo, O. H. Miyagaki and B. Ruf, Elliptic equations in ℝ]^{2} with nonlinearities in the critical growth range, Calc. Var. Partial Differential Equations 3 (1995), 139-153.10.1007/BF01205003
Search in Google Scholar

[
[24] J. M. do, Semilinear Dirichlet problems for the N-Laplacian in ℝ]^{N} with nonlinearities in critical growth range, Differential Integral Equations 5 (1996), 967979.
Search in Google Scholar

[
[25] J. M. do, B. Ruf, On a Schrdinger equation with periodic potential and critical growth in ℝ]^{2}, NoDEA Nonlinear Differential Equations Appl. 13 (2006), 167192.10.1007/s00030-005-0034-3
Search in Google Scholar

[
[26] L. Jeanjean, Solutions in spectral gaps for a nonlinear equation of Schrdinger type, J. Differential Equations 112 (1994), 53-80.10.1006/jdeq.1994.1095
]Search in Google Scholar

[
[27] M. K.-H. Kiessling, Statistical Mechanics of Classical Particles with Logarithmic Interactions, Communications on Pure and Applied Mathematics 46 (1993), 27-56.10.1002/cpa.3160460103
]Search in Google Scholar

[
[28] W. Kryszewski, A. Szulkin, Generalized linking theorem with an application to semilinear Schrdinger equation, Adv. Difference Equ. 3 (1998), 441-472.
]Search in Google Scholar

[
[29] A. Kufner, Weighted Sobolev spaces, John Wiley and Sons Ltd, 1985.
]Search in Google Scholar

[
[30] C.Y. Lei, J.F. Liao, Positive radial symmetric solutions for a class of elliptic problems with critical exponent and -1 growth, Adv. Nonlinear Anal. 10 (2021), no. 1, 1222-1234.
]Search in Google Scholar

[
[31] J. Liouville, Sur l’quation aux derivées partielles, Journal de Mathématiques Pures et Appliquées 18 (1853), 71-72.
]Search in Google Scholar

[
[32] P. L. Lions, The Concentration-compactness principle in the Calculus of Variations, Part 1, Revista Iberoamericana 11 (1985), 185-201.
]Search in Google Scholar

[
[33] N. Masmoudi and F. Sani, Trudinger-Moser inequalities with the exact growth condition in ℝ]^{ℕ} and applications, Comm. Partial Diferential Equations 40 (2015), 1408-1440.10.1080/03605302.2015.1026775
Search in Google Scholar

[
[34] P. Perona and J. Malik, Scale-space and edge detection using anisotropic diffusion, IEEE Transactions on Pattern Analysis and Machine Intelligence 12 (1990), 629-639.10.1109/34.56205
]Search in Google Scholar

[
[35] P. H. Rabinowitz, Mini-max Methods in Critical Point Theory with Applications to Differential Equations, CBMS Reg. Conf. Ser. in Math. No. 65, AMS, Providence (1986).10.1090/cbms/065
]Search in Google Scholar

[
[36] G. Tarantello, Multiple condensate Solutions for the Chern - Simons -Higgs Theory, Journal of Mathematical Physics vol. 37 (1996), 3769-3796.10.1063/1.531601
]Search in Google Scholar

[
[37] G. Tarantello, Analytical Aspects of Liouville-Type Equations with Singular Sources, Handbook of Differential Equations (M. Chipot and P. Quittner, eds.), Elsevier, North Holland 2004, 491-592.10.1016/S1874-5733(04)80009-3
]Search in Google Scholar

[
[38] R. E. Volquer, Nonlinear flow in porus media by finite elements, ASCE Proc, J Hydrailics Division Proc. Am. Soc. Civil Eng., 95 (1969), 2093-2114.
]Search in Google Scholar

[
[39] Y. Yang, Existence of positive solutions to quasi-linear elliptic equations with exponential growth in the whole Euclidean space, J. Funct. Anal. 262 (2012), 1679-1704.10.1016/j.jfa.2011.11.018
]Search in Google Scholar

[
[40] C. Zhang, Concentration-Compactness principle for TrudingerMoser inequalities with logarithmic weights and their applications, Nonlinear Anal. 197 (2020), 1-22.
]Search in Google Scholar