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.
@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},
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     zbl = {05024490},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2005.02.002/}
}
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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] 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 | Zbl

[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 | Zbl

[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 | Zbl

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

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

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

[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 | Zbl

[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 | 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] 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 | Zbl

[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 | 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] Molle R., Passaseo D., 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] 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 | Zbl

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

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

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

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

[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 | Zbl

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

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

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

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

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