Concentration phenomena for solutions of superlinear elliptic problems
Molle, Riccardo ; Passaseo, Donato
Annales de l'I.H.P. Analyse non linéaire, Tome 23 (2006), p. 63-84 / Harvested from Numdam
@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},
     volume = {23},
     year = {2006},
     pages = {63-84},
     doi = {10.1016/j.anihpc.2005.02.002},
     mrnumber = {2194581},
     zbl = {05024490},
     language = {en},
     url = {http://dml.mathdoc.fr/item/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) pp. 63-84. doi : 10.1016/j.anihpc.2005.02.002. http://gdmltest.u-ga.fr/item/AIHPC_2006__23_1_63_0/

[1] Bahri A., Coron J.M., 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] Bahri A., Li Y.Y., Rey O., 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 1384837 | Zbl 0814.35032

[3] Berestycki H., Lions P.L., Nonlinear scalar fields equations - I. Existence of a ground-state, Arch. Rational Mech. Anal. 82 (1983) 313-346. | MR 695535 | Zbl 0533.35029

[4] Brézis H., Elliptic equations with limiting Sobolev exponents - the impact of topology, Comm. Pure Appl. Math. 39 (suppl.) (1986) S17-S39. | MR 861481 | Zbl 0601.35043

[5] Brézis H., Nirenberg L., Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math. 36 (4) (1983) 437-477. | MR 709644 | Zbl 0541.35029

[6] Coron J.M., Topologie et cas limite des injections de Sobolev, C. R. Acad. Sci. Paris Sér. I Math. 299 (7) (1984) 209-212. | MR 762722 | Zbl 0569.35032

[7] Dancer E.N., Zhang K., 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 1780642 | Zbl 0960.35035

[8] Gidas B., Ni W.M., Nirenberg L., Symmetry of positive solutions of nonlinear elliptic equations in R N , in: Mathematical Analysis and Applications - Part A, Advances in Mathematics Supplementary Studies, vol. 7-A, Academic Press, 1981, pp. 369-402. | MR 634248 | Zbl 0469.35052

[9] Kwong M.K., Uniqueness of positive solutions of Δu-u+u p =0, Arch. Rational Mech. Anal. 105 (1989) 243-266. | MR 969899 | Zbl 0676.35032

[10] Lions P.L., 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 778970 | Zbl 0541.49009

[11] Littman W., Stampacchia G., Weinberger H.F., Regular points for elliptic equations with discontinuous coefficients, Ann. Scuola Norm. Sup. Pisa 17 (3) (1963) 43-77. | Numdam | MR 161019 | Zbl 0116.30302

[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 1937113

[13] Molle R., Passaseo D., 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

[14] Molle R., Passaseo D., 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

[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] Molle R., Passaseo D., On the existence of positive solutions of slightly supercritical elliptic equations, Adv. Nonlinear Stud. 3 (3) (2003) 301-326. | MR 1989741 | Zbl 1094.35051

[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] Passaseo D., 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

[19] Passaseo D., Nonexistence results for elliptic problems with supercritical nonlinearity in nontrivial domains, J. Funct. Anal. 114 (1) (1993) 97-105. | MR 1220984 | Zbl 0793.35039

[20] Passaseo D., New nonexistence results for elliptic equations with supercritical nonlinearity, Differential Integral Equations 8 (3) (1995) 577-586. | MR 1306576 | Zbl 0821.35056

[21] Passaseo D., Nontrivial solutions of elliptic equations with supercritical exponent in contractible domains, Duke Math. J. 92 (2) (1998) 429-457. | MR 1612734 | Zbl 0943.35034

[22] Pohožaev S.I., On the eigenfunctions of the equation Δu+λfu=0, Soviet Math. Dokl. 6 (1965) 1408-1411. | MR 192184 | Zbl 0141.30202

[23] Rey O., 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 1040954 | Zbl 0786.35059

[24] Riesz F., Nagy B.Sz., Functional Analysis, Dover, New York, 1990. | MR 1068530 | Zbl 0732.47001

[25] Schaaf R., Uniqueness for semilinear elliptic problems: supercritical growth and domain geometry, Adv. Differential Equations 5 (10-12) (2000) 1201-1220. | MR 1785673 | Zbl 0989.35056

[26] Strauss W.A., Existence of solitary waves in higher dimensions, Comm. Math. Phys. 55 (1977) 149-162. | MR 454365 | Zbl 0356.35028

[27] Talenti G., Best constants in Sobolev inequality, Ann. Mat. Pura Appl. 110 (1976) 353-372. | MR 463908 | Zbl 0353.46018