@article{ASNSP_1999_4_28_1_1_0, author = {Silva, Elves A. de B. and Soares, S\'ergio H. M.}, title = {Liouville-Gelfand type problems for the $N$-laplacian on bounded domains of $\mathbb {R}^N$}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {1--30}, publisher = {Scuola normale superiore}, volume = {Ser. 4, 28}, number = {1}, year = {1999}, mrnumber = {1679076}, zbl = {0943.35032}, language = {en}, url = {http://www.numdam.org/item/ASNSP_1999_4_28_1_1_0/} }
TY - JOUR AU - Silva, Elves A. de B. AU - Soares, Sérgio H. M. TI - Liouville-Gelfand type problems for the $N$-laplacian on bounded domains of $\mathbb {R}^N$ JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 1999 SP - 1 EP - 30 VL - 28 IS - 1 PB - Scuola normale superiore UR - http://www.numdam.org/item/ASNSP_1999_4_28_1_1_0/ LA - en ID - ASNSP_1999_4_28_1_1_0 ER -
%0 Journal Article %A Silva, Elves A. de B. %A Soares, Sérgio H. M. %T Liouville-Gelfand type problems for the $N$-laplacian on bounded domains of $\mathbb {R}^N$ %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 1999 %P 1-30 %V 28 %N 1 %I Scuola normale superiore %U http://www.numdam.org/item/ASNSP_1999_4_28_1_1_0/ %G en %F ASNSP_1999_4_28_1_1_0
Silva, Elves A. de B.; Soares, Sérgio H. M. Liouville-Gelfand type problems for the $N$-laplacian on bounded domains of $\mathbb {R}^N$. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 28 (1999) no. 1, pp. 1-30. http://www.numdam.org/item/ASNSP_1999_4_28_1_1_0/
[ 1 ] 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. | Numdam | MR | Zbl
,[2] 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. | Numdam | MR | Zbl
- ,[3] Dual variational methods in critical point theory and applications, J. Funct. Anal. 14 (1973), 349-381. | MR | Zbl
- ,[4] G., Sur les équations intégrales non linéaires, Bull. Soc. Math. France 42 (1914), 113-142. | JFM | Numdam | MR
,[5] Opérateurs maximaux monotones et semi-groupes de contraction dans les espaces de Hilbert", North Holland, Amsterdam, 1973. | MR | Zbl
, "[6] Positive solutions of nonlinear elliptic equations involving critical exponents, Comm. Pure Appl. Math. 36 (1983), 437-477. | MR | Zbl
- ,[7] Quasilinear elliptic equations with critical exponents, Topol. Methods Nonlinear Anal. 7 (1996), 133-170. | MR | Zbl
- - ,[8] Some continuation and variational methods for positive solutions of nonlinear elliptic eigenvalue problems, Arch. Rat. Mech. Anal. 58 (1975), 201-218. | MR | Zbl
- ,[9] C1,α local regularity of weak solutions of degenerate elliptic equations, Nonlinear Anal. 7, 8 (1983), 827-850. | Zbl
,[10] Quasilinear elliptic equations with exponential nonlinearities, Comm. Appl. Nonlinear Anal. 3 (1995), 63-72. | MR | Zbl
,[11] Elliptic equations in R2 with nonlinearites in the critical growth range, Calc. Var. Partial Differential Equations 3 (1995), 139-153. | MR | Zbl
- - ,[12] On an Emden-Fowler type equation, Nonlinear Anal. 18 (1992), 1085-1997. | MR | Zbl
- ,[13] Some problems in the theory of quasi-linear equations, Amer. Math. Soc. Transl. Ser. 2, 29 (1963), 295-381. | MR
,[14] Elliptic Partial Differential Equations of Second Order, 2nd edition, Springer, Berlin-Heidelberg-New York - Tokio, 1983. | MR | Zbl
- , "[15] The concentration-compactness principle in the calculus of variations. The limit case, Rev. Mat. Iberoamericana 1 (1985), 145-201. | MR | Zbl
,[16] Sur l'equation aux différences partielles d2log λ/dudv ± λ a2 = 0, J. Math. Pures Appl. 18 (1853), 71-72.
,[17] A sharp form of an inequality by N. Trudinger, Indiana Univ. Math. J. 20 (1971), 1077 -1092. | MR | Zbl
,[18] On semilinear Neumann problems with critical growth for the N-Laplacian, Nonlinear Anal. 8 (1996), 1347-1366. | MR | Zbl
,[19] 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). | Zbl
,[20] Real and Complex Analysis", 3d edition, McGraw-Hill Book Company, New York, 1987. | MR | Zbl
, "[21] Linking theorems and applications to semilinear problems at resonance, Nonlinear Anal. 16 (1991), 455-477. | MR | Zbl
,[22] Quasilinear Dirichlet problems in RN with critical growth, To appear in Nonlinear Anal. | Zbl
- ,[23] On imbedding into Orlicz spaces and some applications, J. Math. Mech. 17 (1967), 473-484. | MR | Zbl
,