@article{AIHPC_2006__23_3_389_0, author = {Molle, Riccardo and Passaseo, Donato}, title = {Multiple solutions of supercritical elliptic problems in perturbed domains}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, volume = {23}, year = {2006}, pages = {389-405}, doi = {10.1016/j.anihpc.2005.05.003}, mrnumber = {2217657}, zbl = {05024468}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPC_2006__23_3_389_0} }
Molle, Riccardo; Passaseo, Donato. Multiple solutions of supercritical elliptic problems in perturbed domains. Annales de l'I.H.P. Analyse non linéaire, Tome 23 (2006) pp. 389-405. doi : 10.1016/j.anihpc.2005.05.003. http://gdmltest.u-ga.fr/item/AIHPC_2006__23_3_389_0/
[1] On a nonlinear elliptic equation involving the critical Sobolev exponent: the effect of the topology of the domain, Comm. Pure Appl. Math. 41 (1988) 253-294. | MR 929280 | Zbl 0649.35033
, ,[2] On the Morse indices of sign changing solutions of nonlinear elliptic problems, Math. Z. 233 (4) (2000) 655-677. | MR 1759266 | Zbl 0946.35023
, , ,[3] A remark on the nodal regions of the solutions of some superlinear elliptic equations, Proc. Roy. Soc. Edinburgh Sect. A 111 (1-2) (1989) 123-128. | MR 985994 | Zbl 0686.35043
, ,[4] Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math. 36 (4) (1983) 437-477. | MR 709644 | Zbl 0541.35029
, ,[5] A note on an equation with critical exponent, Bull. London Math. Soc. 20 (6) (1988) 600-602. | MR 980763 | Zbl 0646.35027
,[6] Uniqueness of solutions for some elliptic equations and systems in nearly star-shaped domains, Nonlinear Anal. 41 (5-6) (2000) 745-761. | MR 1780642 | Zbl 0960.35035
, ,[7] Positive solutions of on contractible domains, J. Partial Differential Equations 2 (4) (1989) 83-88. | MR 1027983 | Zbl 0694.35067
,[8] Remarks on some quasilinear elliptic equations, Comm. Pure Appl. Math. 28 (5) (1975) 567-597. | MR 477445 | Zbl 0325.35038
, ,[9] Topological Methods in the Theory of Nonlinear Integral Equations, A Pergamon Press Book, The Macmillan Co., New York, 1964, (Translation edited by J. Burlak). | MR 159197 | Zbl 0111.30303
,[10] Positive solutions for slightly super-critical elliptic equations in contractible domains, Preprint Dip. Matem. Univ. Lecce, n. 6, 2001 and, C. R. Acad. Sci. Paris Sér. I Math. 335 (5) (2002) 459-462. | MR 1937113 | Zbl 1010.35043
, ,[11] Nonlinear elliptic equations with critical Sobolev exponent in nearly starshaped domains, C. R. Acad. Sci. Paris Sér. I Math. 335 (12) (2002) 1029-1032. | MR 1955582 | Zbl 1032.35071
, ,[12] Positive solutions of slightly supercritical elliptic equations in symmetric domains, Ann. Inst. H. Poincaré Anal. Non Linéaire 21 (5) (2004) 639-656. | Numdam | MR 2086752 | Zbl 02116182
, ,[13] On the existence of positive solutions of slightly supercritical elliptic equations, Adv. Nonlinear Stud. 3 (3) (2003) 301-326. | MR 1989741 | Zbl 1094.35051
, ,[14] R. Molle, D. Passaseo, Nonlinear elliptic equations with large supercritical exponents, Preprint Dip. Mat. Università di Roma “Tor Vergata”, 2003; Calc. Var. Partial Differential Equations, submitted for publication. | Zbl 1093.35022
[15] R. Molle, D. Passaseo, in preparation.
[16] Multiplicity of positive solutions of nonlinear elliptic equations with critical Sobolev exponent in some contractible domains, Manuscripta Math. 65 (2) (1989) 147-165. | MR 1011429 | Zbl 0701.35068
,[17] Nonexistence results for elliptic problems with supercritical nonlinearity in nontrivial domains, J. Funct. Anal. 114 (1) (1993) 97-105. | MR 1220984 | Zbl 0793.35039
,[18] The effect of the domain shape on the existence of positive solutions of the equation , Topol. Methods Nonlinear Anal. 3 (1) (1994) 27-54. | MR 1272886 | Zbl 0812.35032
,[19] New nonexistence results for elliptic equations with supercritical nonlinearity, Differential Integral Equations 8 (3) (1995) 577-586. | MR 1306576 | Zbl 0821.35056
,[20] Nontrivial solutions of elliptic equations with supercritical exponent in contractible domains, Duke Math. J. 92 (2) (1998) 429-457. | MR 1612734 | Zbl 0943.35034
,[21] On the eigenfunctions of the equation , Soviet Math. Dokl. 6 (1965) 1408-1411. | MR 192184 | Zbl 0141.30202
,