Liouville-Gelfand type problems for the $N$-laplacian on bounded domains of ${ℝ}^N$

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1. [ 1 ] Adimurthi, Existence of positive solutions of the semilinear Dirichlet problems with critical growth for the N-Laplacian, Ann. Sc. Norm. Sup. Pisa Cl. Sci. (4) 17 (1990), 393-413. Zbl0732.35028MR1079983
2. [2] Adimurthi - S.L. Yadava, Multiplicity results for semilinear elliptic equations in a bounded domain of R2 involving critical exponent, Ann. Sc. Norm. Sup. Pisa Cl. Sci. (4) 17 (1990), 481-504. Zbl0732.35029MR1093706
3. [3] A. Ambrosetti - P.H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal.14 (1973), 349-381. Zbl0273.49063MR370183
4. [4] G. Bratu, G., Sur les équations intégrales non linéaires, Bull. Soc. Math. France42 (1914), 113-142. Zbl45.0525.03MR1504727JFM45.1306.01
5. [5] H. Brezis, "Opérateurs maximaux monotones et semi-groupes de contraction dans les espaces de Hilbert", North Holland, Amsterdam, 1973. Zbl0252.47055MR348562
6. [6] H. Brezis - L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical exponents, Comm. Pure Appl. Math.36 (1983), 437-477. Zbl0541.35029MR709644
7. [7] P. Clément - D.G. De Figueiredo - E. Mitidieri, Quasilinear elliptic equations with critical exponents, Topol. Methods Nonlinear Anal.7 (1996), 133-170. Zbl0939.35072MR1422009
8. [8] M.G. Crandall - P.H. Rabinowitz, Some continuation and variational methods for positive solutions of nonlinear elliptic eigenvalue problems, Arch. Rat. Mech. Anal.58 (1975), 201-218. Zbl0309.35057MR382848
9. [9] E. Dibenedetto, C1,α local regularity of weak solutions of degenerate elliptic equations, Nonlinear Anal.7, 8 (1983), 827-850. Zbl0539.35027
10. [10] J.M.B. Do Ó, Quasilinear elliptic equations with exponential nonlinearities, Comm. Appl. Nonlinear Anal.3 (1995), 63-72. Zbl0858.35042MR1343597
11. [11] D.G. De Figueiredo - O.H. Miyagaki - B. Ruf, Elliptic equations in R2 with nonlinearites in the critical growth range, Calc. Var. Partial Differential Equations3 (1995), 139-153. Zbl0820.35060MR1386960
12. [12] J. Garcia Azorero - I. Peral Alonso, On an Emden-Fowler type equation, Nonlinear Anal.18 (1992), 1085-1997. Zbl0781.35021MR1167423
13. [13] I.M. Gelfand, Some problems in the theory of quasi-linear equations, Amer. Math. Soc. Transl. Ser.2, 29 (1963), 295-381. MR153960
14. [14] D. Gilbarg - N.S. Trudinger, "Elliptic Partial Differential Equations of Second Order, 2nd edition, Springer, Berlin-Heidelberg-New York - Tokio, 1983. Zbl0562.35001MR737190
15. [15] P.L. Lions, The concentration-compactness principle in the calculus of variations. The limit case, Rev. Mat. Iberoamericana1 (1985), 145-201. Zbl0704.49005MR834360
16. [16] J. Liouville, Sur l'equation aux différences partielles d2log λ/dudv ± λ a2 = 0, J. Math. Pures Appl.18 (1853), 71-72. 
17. [17] J. Moser, A sharp form of an inequality by N. Trudinger, Indiana Univ. Math. J.20 (1971), 1077 -1092. Zbl0203.43701MR301504
18. [18] R. Panda, On semilinear Neumann problems with critical growth for the N-Laplacian, Nonlinear Anal.8 (1996), 1347-1366. Zbl0854.35045MR1377667
19. [19] P.H. Rabinowitz, Minimax methods in critical point theory with applications to diff. equations, CBMS Regional Confer. Ser. in Math. n° 65, Amer. Math. Soc.Providence, RI (1986). Zbl0609.58002
20. [20] W. Rudin, "Real and Complex Analysis", 3d edition, McGraw-Hill Book Company, New York, 1987. Zbl0925.00005MR924157
21. [21] E.A.B. Silva, Linking theorems and applications to semilinear problems at resonance, Nonlinear Anal.16 (1991), 455-477. Zbl0731.35042MR1093380
22. [22] E.A.B. Silva - S.H.M. Soares, Quasilinear Dirichlet problems in RN with critical growth, To appear in Nonlinear Anal. Zbl1158.35368
23. [23] N. Trudinger, On imbedding into Orlicz spaces and some applications, J. Math. Mech.17 (1967), 473-484. Zbl0163.36402MR216286