Concentration phenomena for solutions of superlinear elliptic problems

 Access to full text

 Full (PDF)

1. [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. Zbl0649.35033MR929280
2. [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. Zbl0814.35032MR1384837
3. [3] Berestycki H., Lions P.L., Nonlinear scalar fields equations – I. Existence of a ground-state, Arch. Rational Mech. Anal.82 (1983) 313-346. Zbl0533.35029MR695535
4. [4] Brézis H., Elliptic equations with limiting Sobolev exponents – the impact of topology, Comm. Pure Appl. Math.39 (suppl.) (1986) S17-S39. Zbl0601.35043MR861481
5. [5] Brézis H., Nirenberg L., Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math.36 (4) (1983) 437-477. Zbl0541.35029MR709644
6. [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. Zbl0569.35032MR762722
7. [7] Dancer E.N., Zhang K., Uniqueness of solutions for some elliptic equations and systems in nearly star-shaped domains, Nonlinear Anal. Ser. A41 (5/6) (2000) 745-761. Zbl0960.35035MR1780642
8. [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. Zbl0469.35052MR634248
9. [9] Kwong M.K., Uniqueness of positive solutions of $\Delta u-u+u^p=0$, Arch. Rational Mech. Anal.105 (1989) 243-266. Zbl0676.35032MR969899
10. [10] Lions P.L., The concentration-compactness principle in the calculus of variations. The locally compact case. I, Ann. Inst. H. Poincaré Anal. Non Linéaire1 (2) (1984) 109-145. Zbl0541.49009MR778970
11. [11] Littman W., Stampacchia G., Weinberger H.F., Regular points for elliptic equations with discontinuous coefficients, Ann. Scuola Norm. Sup. Pisa17 (3) (1963) 43-77. Zbl0116.30302MR161019
12. [12] R. Molle, D. Passaseo, Positive solutions for slightly super-critical elliptic equations in contractible domains, Preprint Dip. Matem. Univ. Lecce, n. 6, 2001. Zbl1010.35043MR1937113
13. [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. Zbl1032.35071MR1955582
14. [14] Molle R., Passaseo D., Positive solutions of slightly supercritical elliptic equations in symmetric domains, Ann. Inst. H. Poincaré Anal. Non Linéaire21 (5) (2004) 639-656. Zbl1149.35353MR2086752
15. [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. Zbl1221.35119
16. [16] Molle R., Passaseo D., On the existence of positive solutions of slightly supercritical elliptic equations, Adv. Nonlinear Stud.3 (3) (2003) 301-326. Zbl1094.35051MR1989741
17. [17] R. Molle, D. Passaseo, Nonlinear elliptic equations with large supercritical exponents, Preprint del Dipartimento di Matematica dell'Università di Roma “Tor Vergata”, 2003. Zbl1093.35022
18. [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. Zbl0701.35068MR1011429
19. [19] Passaseo D., Nonexistence results for elliptic problems with supercritical nonlinearity in nontrivial domains, J. Funct. Anal.114 (1) (1993) 97-105. Zbl0793.35039MR1220984
20. [20] Passaseo D., New nonexistence results for elliptic equations with supercritical nonlinearity, Differential Integral Equations8 (3) (1995) 577-586. Zbl0821.35056MR1306576
21. [21] Passaseo D., Nontrivial solutions of elliptic equations with supercritical exponent in contractible domains, Duke Math. J.92 (2) (1998) 429-457. Zbl0943.35034MR1612734
22. [22] Pohožaev S.I., On the eigenfunctions of the equation $\Delta u+\lambda f\left(u\right)=0$, Soviet Math. Dokl.6 (1965) 1408-1411. Zbl0141.30202MR192184
23. [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. Zbl0786.35059MR1040954
24. [24] Riesz F., Nagy B.Sz., Functional Analysis, Dover, New York, 1990. Zbl0732.47001MR1068530
25. [25] Schaaf R., Uniqueness for semilinear elliptic problems: supercritical growth and domain geometry, Adv. Differential Equations5 (10–12) (2000) 1201-1220. Zbl0989.35056MR1785673
26. [26] Strauss W.A., Existence of solitary waves in higher dimensions, Comm. Math. Phys.55 (1977) 149-162. Zbl0356.35028MR454365
27. [27] Talenti G., Best constants in Sobolev inequality, Ann. Mat. Pura Appl.110 (1976) 353-372. Zbl0353.46018MR463908