@article{AIHPC_2006__23_1_63_0, author = {Molle, Riccardo and Passaseo, Donato}, title = {Concentration phenomena for solutions of superlinear elliptic problems}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {63--84}, publisher = {Elsevier}, volume = {23}, number = {1}, year = {2006}, doi = {10.1016/j.anihpc.2005.02.002}, mrnumber = {2194581}, zbl = {05024490}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2005.02.002/} }
TY - JOUR AU - Molle, Riccardo AU - Passaseo, Donato TI - Concentration phenomena for solutions of superlinear elliptic problems JO - Annales de l'I.H.P. Analyse non linéaire PY - 2006 SP - 63 EP - 84 VL - 23 IS - 1 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpc.2005.02.002/ DO - 10.1016/j.anihpc.2005.02.002 LA - en ID - AIHPC_2006__23_1_63_0 ER -
%0 Journal Article %A Molle, Riccardo %A Passaseo, Donato %T Concentration phenomena for solutions of superlinear elliptic problems %J Annales de l'I.H.P. Analyse non linéaire %D 2006 %P 63-84 %V 23 %N 1 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpc.2005.02.002/ %R 10.1016/j.anihpc.2005.02.002 %G en %F AIHPC_2006__23_1_63_0
Molle, Riccardo; Passaseo, Donato. Concentration phenomena for solutions of superlinear elliptic problems. Annales de l'I.H.P. Analyse non linéaire, Tome 23 (2006) no. 1, pp. 63-84. doi : 10.1016/j.anihpc.2005.02.002. http://archive.numdam.org/articles/10.1016/j.anihpc.2005.02.002/
[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 | Zbl
, ,[2] On a variational problem with lack of compactness: the topological effect of the critical points at infinity, Calc. Var. 3 (1) (1995) 67-93. | MR | Zbl
, , ,[3] Nonlinear scalar fields equations - I. Existence of a ground-state, Arch. Rational Mech. Anal. 82 (1983) 313-346. | MR | Zbl
, ,[4] Elliptic equations with limiting Sobolev exponents - the impact of topology, Comm. Pure Appl. Math. 39 (suppl.) (1986) S17-S39. | MR | Zbl
,[5] Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math. 36 (4) (1983) 437-477. | MR | Zbl
, ,[6] Topologie et cas limite des injections de Sobolev, C. R. Acad. Sci. Paris Sér. I Math. 299 (7) (1984) 209-212. | MR | Zbl
,[7] Uniqueness of solutions for some elliptic equations and systems in nearly star-shaped domains, Nonlinear Anal. Ser. A 41 (5/6) (2000) 745-761. | MR | Zbl
, ,[8] Symmetry of positive solutions of nonlinear elliptic equations in , in: Mathematical Analysis and Applications - Part A, Advances in Mathematics Supplementary Studies, vol. 7-A, Academic Press, 1981, pp. 369-402. | MR | Zbl
, , ,[9] Uniqueness of positive solutions of , Arch. Rational Mech. Anal. 105 (1989) 243-266. | MR | Zbl
,[10] The concentration-compactness principle in the calculus of variations. The locally compact case. I, Ann. Inst. H. Poincaré Anal. Non Linéaire 1 (2) (1984) 109-145. | Numdam | MR | Zbl
,[11] Regular points for elliptic equations with discontinuous coefficients, Ann. Scuola Norm. Sup. Pisa 17 (3) (1963) 43-77. | Numdam | MR | Zbl
, , ,[12] R. Molle, D. Passaseo, Positive solutions for slightly super-critical elliptic equations in contractible domains, Preprint Dip. Matem. Univ. Lecce, n. 6, 2001. | MR
[13] 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 | Zbl
, ,[14] Positive solutions of slightly supercritical elliptic equations in symmetric domains, Ann. Inst. H. Poincaré Anal. Non Linéaire 21 (5) (2004) 639-656. | Numdam | MR | Zbl
, ,[15] R. Molle, D. Passaseo, Multispike solutions of nonlinear elliptic equations with critical Sobolev exponent, Preprint del Dipartimento di Matematica dell'Università di Roma “Tor Vergata”, 2003.
[16] On the existence of positive solutions of slightly supercritical elliptic equations, Adv. Nonlinear Stud. 3 (3) (2003) 301-326. | MR | Zbl
, ,[17] R. Molle, D. Passaseo, Nonlinear elliptic equations with large supercritical exponents, Preprint del Dipartimento di Matematica dell'Università di Roma “Tor Vergata”, 2003.
[18] Multiplicity of positive solutions of nonlinear elliptic equations with critical Sobolev exponent in some contractible domains, Manuscripta Math. 65 (2) (1989) 147-165. | MR | Zbl
,[19] Nonexistence results for elliptic problems with supercritical nonlinearity in nontrivial domains, J. Funct. Anal. 114 (1) (1993) 97-105. | MR | Zbl
,[20] New nonexistence results for elliptic equations with supercritical nonlinearity, Differential Integral Equations 8 (3) (1995) 577-586. | MR | Zbl
,[21] Nontrivial solutions of elliptic equations with supercritical exponent in contractible domains, Duke Math. J. 92 (2) (1998) 429-457. | MR | Zbl
,[22] On the eigenfunctions of the equation , Soviet Math. Dokl. 6 (1965) 1408-1411. | MR | Zbl
,[23] The role of the Green's function in a nonlinear elliptic equation involving the critical Sobolev exponent, J. Funct. Anal. 89 (1) (1990) 1-52. | MR | Zbl
,[24] Functional Analysis, Dover, New York, 1990. | MR | Zbl
, ,[25] Uniqueness for semilinear elliptic problems: supercritical growth and domain geometry, Adv. Differential Equations 5 (10-12) (2000) 1201-1220. | MR | Zbl
,[26] Existence of solitary waves in higher dimensions, Comm. Math. Phys. 55 (1977) 149-162. | MR | Zbl
,[27] Best constants in Sobolev inequality, Ann. Mat. Pura Appl. 110 (1976) 353-372. | MR | Zbl
,Cité par Sources :