Sign changing bubble tower solutions in a slightly subcritical semilinear Dirichlet problem

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1. [1] Atkinson F.V., Brezis H., Peletier L.A., Solutions d'équations elliptiques avec exposant de Sobolev critique qui changent de signe, C. R. Acad. Sci. Paris306 (1988) 711-714. Zbl0696.35059MR944417
2. [2] Atkinson F.V., Brezis H., Peletier L.A., Nodal solutions of elliptic equations with critical Sobolev exponents, J. Differential Equations85 (1990) 151-170. Zbl0702.35099MR1052332
3. [3] Aubin T., Problèmes isoperimetriques et espaces de Sobolev, J. Differential Geom.11 (1976) 573-598. Zbl0371.46011MR448404
4. [4] Bahri A., Critical Points at Infinity in Some Variational Problems, Pitman Research Notes in Mathematics Series, vol. 182, Longman, 1989. Zbl0676.58021MR1019828
5. [5] 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 (3) (1988) 253-294. Zbl0649.35033MR929280
6. [6] Bahri A., Li Y., Rey O., On a variational problem with lack of compactness: the topological effect of the critical points at infinity, Calc. Var. Partial Differential Equations3 (1995) 67-93. Zbl0814.35032MR1384837
7. [7] Bartsch T., Critical point theory on partially ordered Hilbert spaces, J. Funct. Anal.186 (2001) 117-152. Zbl1211.58003MR1863294
8. [8] Bartsch T., Wang Z.-Q., On the existence of sign changing solutions for semilinear Dirichlet problems, Topol. Methods Nonlinear Anal.7 (1996) 115-131. Zbl0903.58004MR1422008
9. [9] Bartsch T., Weth T., A note on additional properties of sign changing solutions to superlinear elliptic equations, Topol. Methods Nonlinear Anal.22 (2003) 1-14. Zbl1094.35041MR2037264
10. [10] Bartsch T., Micheletti A.M., Pistoia A., On the existence and the profile of nodal solutions of elliptic equations involving critical growth, Calc. Var. Partial Differential Equations26 (3) (2006) 265-282. Zbl1104.35009MR2232205
11. [11] Ben Ayed M., El Mehdi K., Grossi M., Rey O., A nonexistence result of single peaked solutions to a supercritical nonlinear problem, Comm. Contemp. Math.5 (2) (2003) 179-195. Zbl1066.35035MR1966257
12. [12] Bianchi G., Egnell H., A note on the Sobolev inequality, J. Funct. Anal.100 (1991) 18-24. Zbl0755.46014MR1124290
13. [13] Brézis H., Peletier L.A., Asymptotics for elliptic equations involving critical growth, in: Partial Differential Equations and the Calculus of Variations, vol. I, Progr. Nonlinear Differential Equations Appl., vol. 1, Birkhäuser, Boston, MA, 1996, pp. 149-192. Zbl0685.35013MR1034005
14. [14] Caffarelli L., Gidas B., Spruck J., Asymptotic symmetry and local behaviour of semilinear elliptic equations with critical Sobolev growth, Comm. Pure Appl. Math.42 (1989) 271-297. Zbl0702.35085MR982351
15. [15] Castro A., Clapp M., The effect of the domain topology on the number of minimal nodal solutions of an elliptic equation at critical growth in a symmetric domain, Nonlinearity16 (2003) 579-590. Zbl1108.35054MR1959099
16. [16] Castro A., Cossio J., Neuberger J.M., A sign-changing solution for a superlinear Dirichlet problem, Rocky Mountain J. Math.27 (1997) 1041-1053. Zbl0907.35050MR1627654
17. [17] Cerami G., Solimini S., Struwe M., Some existence results for superlinear elliptic boundary value problems involving critical exponents, J. Funct. Anal.69 (1986) 298-306. Zbl0614.35035MR867663
18. [18] Clapp M., Weth T., Multiple solutions for the Brezis–Nirenberg problem, Adv. Differential Equations10 (4) (2005) 463-480. Zbl1284.35151
19. [19] Clapp M., Weth T., Minimal nodal solutions of the pure critical exponent problem on a symmetric domain, Calc. Var. Partial Differential Equations21 (1) (2004) 1-14. Zbl1097.35048MR2078744
20. [20] del Pino M., Dolbeault J., Musso M., “Bubble-tower” radial solutions in the slightly supercritical Brezis–Nirenberg problem, J. Differential Equations193 (2) (2003) 280-306. Zbl1140.35413
21. [21] del Pino M., Dolbeault J., Musso M., The Brezis–Nirenberg problem near criticality in dimension 3, J. Math. Pures Appl. (9)83 (12) (2004) 1405-1456. Zbl1130.35040
22. [22] del Pino M., Felmer P., Musso M., Two-bubble solutions in the super-critical Bahri–Coron's problem, Calc. Var. Partial Differential Equations16 (2003) 113-145. Zbl1142.35421
23. [23] del Pino M., Felmer P., Musso M., Multi-bubble solutions for slightly super-critical elliptic problems in domains with symmetries, Bull. London Math. Soc.35 (2003) 513-521. Zbl1109.35334MR1979006
24. [24] del Pino M., Musso M., Pistoia A., Super-critical boundary bubbling in a semilinear Neumann problem, Ann. Inst. H. Poincaré Anal. Non Linéaire22 (1) (2005) 45-82. Zbl1130.35064MR2114411
25. [25] Ding W.Y., On a conformally invariant elliptic equation on $R^N$, Comm. Math. Phys.107 (1986) 331-335. Zbl0608.35017MR863646
26. [26] Flucher M., Wei J., Semilinear Dirichlet problem with nearly critical exponent, asymptotic location of hot spots, Manuscripta Math.94 (1997) 337-346. Zbl0892.35061MR1485441
27. [27] Fortunato D., Jannelli E., Infinitely many solutions for some nonlinear elliptic problems in symmetrical domains, Proc. Roy. Soc. Edinburgh105 (1987) 205-213. Zbl0676.35024MR890056
28. [28] Ge Y., Jing R., Pacard F., Bubble towers for supercritical semilinear elliptic equations, J. Funct. Anal.221 (2) (2005) 251-302. Zbl1129.35379MR2124865
29. [29] Han Z.C., Asymptotic approach to singular solutions for nonlinear elliptic equations involving critical Sobolev exponent, Ann. Inst. H. Poincaré Anal. Non Linéaire8 (1991) 159-174. Zbl0729.35014MR1096602
30. [30] Hebey E., Vaugon M., Existence and multiplicity of nodal solutions for nonlinear elliptic equations with critical Sobolev growth, J. Funct. Anal.119 (1994) 298-318. Zbl0798.35052MR1261094
31. [31] Hirano N., Micheletti A.M., Pistoia A., Existence of changing-sign solutions for some critical problems on $R^N$, Comm. Pure Appl. Anal.4 (1) (2005) 143-164. Zbl1123.35019MR2126282
32. [32] Kazdan J., Warner F.W., Remarks on some quasilinear elliptic equations, Comm. Pure Appl. Math.28 (1975) 567-597. Zbl0325.35038MR477445
33. [33] Li Y.Y., Prescribing scalar curvature on $S^n$ and related problems. I, J. Differential Equations120 (2) (1995) 319-410. Zbl0827.53039MR1347349
34. [34] Micheletti A.M., Pistoia A., On the effect of the domain geometry on the existence of sign changing solutions to elliptic problems with critical and supercritical growth, Nonlinearity17 (3) (2004) 851-866. Zbl1102.35042MR2057131
35. [35] Molle R., Passaseo D., Positive solutions for slightly super-critical elliptic equations in contractible domains, C. R. Math. Acad. Sci. Paris, Ser. I335 (2002) 459-462. Zbl1010.35043MR1937113
36. [36] Müller-Pfeiffer E., On the number of nodal domains for elliptic differential operators, J. London Math. Soc. (2)31 (1985) 91-100. Zbl0579.35063MR810566
37. [37] Musso M., Pistoia A., Multispike solutions for a nonlinear elliptic problem involving critical Sobolev exponent, Indiana Univ. Math. J.5 (2002) 541-579. Zbl1074.35037MR1911045
38. [38] A. Pistoia, O. Rey, Multiplicity of solutions to the supercritical Bahri–Coron's problem in pierced domains, Adv. Differential Equations, in press. Zbl1166.35333
39. [39] Pohožaev S.I., On the eigenfunctions of the equation $\Delta u+\lambda f\left(u\right)=0$, Dokl. Akad. Nauk SSSR165 (1965) 36-39, (in Russian). Zbl0141.30202MR192184
40. [40] Rey O., Blow-up points of solutions to elliptic equations with limiting nonlinearity, Differential Integral Equations4 (1991) 1155-1167. Zbl0830.35043MR1133750
41. [41] Rey O., The role of the Green's function in a nonlinear elliptic equation involving the critical Sobolev exponent, J. Funct. Anal.89 (1990) 1-52. Zbl0786.35059MR1040954
42. [42] Rey O., Proof of two conjectures of H. Brezis and L.A. Peletier, Manuscripta Math.65 (1989) 19-37. Zbl0708.35032MR1006624
43. [43] Talenti G., Best constants in Sobolev inequality, Ann. Mat. Pura Appl.110 (1976) 353-372. Zbl0353.46018MR463908