@article{AIHPC_2009__26_2_397_0, author = {Cingolani, Silvia and Vannella, Giuseppina}, title = {Multiple {Positive} {Solutions} for a {Critical} {Quasilinear} {Equation} {Via} {Morse} {Theory}}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {397--413}, publisher = {Elsevier}, volume = {26}, number = {2}, year = {2009}, doi = {10.1016/j.anihpc.2007.09.003}, mrnumber = {2504036}, zbl = {1171.35042}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2007.09.003/} }
TY - JOUR AU - Cingolani, Silvia AU - Vannella, Giuseppina TI - Multiple Positive Solutions for a Critical Quasilinear Equation Via Morse Theory JO - Annales de l'I.H.P. Analyse non linéaire PY - 2009 SP - 397 EP - 413 VL - 26 IS - 2 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpc.2007.09.003/ DO - 10.1016/j.anihpc.2007.09.003 LA - en ID - AIHPC_2009__26_2_397_0 ER -
%0 Journal Article %A Cingolani, Silvia %A Vannella, Giuseppina %T Multiple Positive Solutions for a Critical Quasilinear Equation Via Morse Theory %J Annales de l'I.H.P. Analyse non linéaire %D 2009 %P 397-413 %V 26 %N 2 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpc.2007.09.003/ %R 10.1016/j.anihpc.2007.09.003 %G en %F AIHPC_2009__26_2_397_0
Cingolani, Silvia; Vannella, Giuseppina. Multiple Positive Solutions for a Critical Quasilinear Equation Via Morse Theory. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 2, pp. 397-413. doi : 10.1016/j.anihpc.2007.09.003. http://archive.numdam.org/articles/10.1016/j.anihpc.2007.09.003/
[1] Multiplicity of Positive Solutions to a P-Laplacian Equation Involving Critical Nonlinearity, J. Math. Anal. Appl. 279 (2003) 508-521. | MR
, ,[2] Simplicite Et Isolation De La Premiere Valeur Du P-Laplacien Avec Poids, C. R. Acad. Sci. Paris Sér I Math. 305 (1987) (2003) 725-728. | MR | Zbl
,[3] Existence and Nonuniqueness for the P-Laplacian: Nonlinear Eigenvalues, Comm. Partial Differential Equations 12 (1987) 1389-1430. | MR | Zbl
, ,[4] Multiplicity of Solutions for Elliptic Problems With Critical Exponents Or With a Symmetric Term, Trans. Amer. Math. Soc. 323 (1991) 77-895. | MR | Zbl
, ,[5] A New Approach to the Morse-Conley Theory and Some Applications, Ann. Mat. Pura Appl. 158 (1991) 231-305. | MR | Zbl
,[6] The Effect of the Domain Topology on the Number of Positive Solutions of Nonlinear Elliptic Problems, Arch. Rational Mech. Anal. 114 (1991) 79-93. | MR | Zbl
, ,[7] Multiple Positive Solutions of Some Elliptic Problems Via the Morse Theory and the Domain Topology, Calc. Var. Partial Differential Equations 2 (1994) 29-48. | MR | Zbl
, ,[8] A Relation Between Pointwise Convergence of Functions and Convergence of Functional, Proc. Amer. Math. Soc. 88 (1983) 486-490. | MR | Zbl
, ,[9] Positive Solutions of Nonlinear Elliptic Equations Involving Critical Sobolev Exponents, Comm. Pure Appl. Math. 36 (1983) 437-477. | MR | Zbl
, ,[10] Solutions of Asymptotically Linear Operator Equations Via Morse Theory, Comm. Pure Appl. Math. 34 (1981) 693-712. | MR | Zbl
,[11] Infinite Dimensional Morse Theory and Multiple Solution Problems, Birkhäuser, Boston, 1993. | MR | Zbl
,[12] Morse Theory in Nonlinear Analysis, in: , , (Eds.), Nonlinear Functional Analysis and Applications to Differential Equations, World Scientific, Singapore, 1998. | MR | Zbl
,[13] Nontrivial Solutions for P-Laplace Equations With Right Hand Side Having P-Linear Growth at Infinity, Comm. Partial Differential Equations 30 (2005) 1191-1203. | MR | Zbl
, ,[14] Multiplicity Results for a Quasilinear Elliptic System Via Morse Theory, Commun. Contemp. Math. 7 (2005) 227-249. | MR | Zbl
, , ,[15] Critical Groups Computations on a Class of Sobolev Banach Spaces Via Morse Index, Ann. Inst. H. Poincaré Anal. Non Linéaire 20 (2003) 271-292. | EuDML | Numdam | MR | Zbl
, ,[16] Morse Index Computations for a Class of Functionals Defined in Banach Spaces, in: , , (Eds.), Nonlinear Equations: Methods, Models and Applications, Bergamo 2001, Progr. Nonlinear Differential Equations Appl., vol. 54, Birkhäuser, Boston, 2003, pp. 107-116. | MR | Zbl
, ,[17] Marino-Prodi Perturbation Type Results and Morse Indices of Minimax Critical Points for a Class of Functionals in Banach Spaces, Ann. Mat. Pura Appl. 186 (2007) 157-185. | MR | Zbl
, ,[18] Morse Index and Critical Groups for P-Laplace Equations With Critical Exponents, Mediterr. J. Math. 3 (2006) 495-512. | MR | Zbl
, ,[19] Normed Linear Spaces, Springer-Verlag, Berlin, 1973. | MR | Zbl
,[20] Linking Over Cones and Nontrivial Solutions for P-Laplace Equations With P-Superlinear Nonlinearity, Ann. Inst. H. Poincaré Anal. Non Linéaire 24 (2007) 907-919. | EuDML | Numdam | MR | Zbl
, ,[21] M. Degiovanni, S. Lancelotti, in preparation.
[22] Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, 1998. | Zbl
, ,[23] Quasilinear Elliptic Equations Involving Critical Sobolev Exponents, Nonlinear Anal. T.M.A. 13 (1989) 879-902. | MR | Zbl
, ,[24] Solutions Positives Multiples Pour Une Équation Elliptique Non Linéaire Avec L'exposant Critique De Sobolev, C. R. Acad. Sci. Paris Sér. I Math. 314 (1992) 61-64. | MR | Zbl
,[25] Boundary Regularity for Solutions of Degenerate Elliptic Equations, Nonlinear Anal. 12 (1988) 1203-1219. | MR | Zbl
,[26] Metodi Perturbativi Nella Teoria Di Morse, Boll. U.M.I. (4) 11 (Suppl.) 3 (1975) 1-32. | MR | Zbl
, ,[27] Quasilinear Elliptic Problems With Critical Exponents, Nonlinear Anal. T.M.A. 20 (1993) 285-301. | MR | Zbl
, , ,[28] Multiplicity of Positive Solutions for the Equation in Noncontractible Domains, Topol. Methods Nonlinear Anal. 2 (1993) 343-366. | MR | Zbl
,[29] P-Laplacian Problems With Critical Sobolev Exponents, Nonlinear Anal. 66 (2007) 454-459. | MR | Zbl
, ,[30] Eigenfunctions for the Equations , Soviet Math. Dokl. 6 (1965) 1408-1411. | Zbl
,[31] A Multiplicity Result for a Variational Problem With Lack of Compactness, Nonlinear Anal. 13 (1989) 1241-1249. | MR | Zbl
,[32] The Role of Green's Function in a Nonlinear Equation Involving the Critical Sobolev Exponent, J. Funct. Anal. 89 (1990) 1-52. | MR | Zbl
,[33] Multiplicity of Solutions for Quasilinear Elliptic Problems Involving Critical Sobolev Exponents, Ann. Inst. H. Poincaré Anal. Non Linéaire 20 (2) (2003) 341-358. | EuDML | Numdam | MR | Zbl
, ,[34] An Infinite Dimensional Version of Sard's Theorem, Amer. J. Math. 87 (1965) 861-866. | MR | Zbl
,[35] Variational Methods, third ed., Springer-Verlag, Berlin, 1998. | Zbl
,[36] Regularity for a More General Class of Quasilinear Elliptic Equations, J. Differential Equations 51 (1984) 126-150. | MR | Zbl
,[37] On the Dirichlet Problem for a Quasilinear Equations in Domains With Conical Boundary Points, Comm. Partial Differential Equations 8 (1983) 773-817. | MR | Zbl
,[38] Morse Theory on Banach Manifolds, J. Funct. Anal. 10 (1972) 430-445. | MR | Zbl
,[39] A Strong Maximum Principle for Some Quasilinear Elliptic Equations, Appl. Math. Optim. 12 (1984) 191-202. | MR | Zbl
,Cité par Sources :