A nonexistence result for Yamabe type problems on thin annuli

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1. [1] Ahmedou M., El Mehdi K., Computation of the difference of topology at infinity for Yamabe-type problems on annuli-domains, I, Duke Math. J.94 (1998) 215-229. Zbl0966.35043MR1638658
2. [2] Bahri A., Critical Point at Infinity in Some Variational Problems, Pitman Res. Notes Math. Ser., 182, Longman, Harlow, 1989. Zbl0676.58021MR1019828
3. [3] Bahri A., Coron J.M., On a nonlinear elliptic equation involving the critical Sobolev exponent: the effect of topology of the domain, Comm. Pure Appl. Math.41 (1988) 255-294. Zbl0649.35033MR929280
4. [4] Bahri A., Li Y.Y., Rey O., On a variational problem with lack of compactness: the topological effect of critical points at infinity, Calc. Var.3 (1995) 67-93. Zbl0814.35032MR1384837
5. [5] Beauzamy B., Introduction to Banach Spaces and Their Topology, North-Holland, 1983. 
6. [6] Brezis H., Points Critiques Dans les Problèmes Variationnels Sans Compacité, Séminaire Bourbaki, 40eme année, 698, 1987 1988. Zbl0860.58007MR992212
7. [7] Caffarelli L., Gidas B., Spruck J., Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth, Comm. Pure Appl. Math.42 (1989) 271-297. Zbl0702.35085MR982351
8. [8] Dancer E.N., A note on an equation with critical exponent, Bull. London Math. Soc.20 (1988) 600-602. Zbl0646.35027MR980763
9. [9] Ding W.Y., Positive solution of Δu+un+2/n−2=0 on contractible domain, J. Partial Differenial Equations2 (4) (1989) 83-88. Zbl0694.35067
10. [10] Harrabi A., Rebhi S., Selmi A., Solutions of superlinear elliptic equations and their Morse indices, I, Duke Math. J.94 (1998) 141-157. Zbl0952.35042MR1635912
11. [11] Harrabi A., Rebhi S., Selmi A., Solutions of superlinear elliptic equations and their Morse indices, II, Duke Math. J.94 (1998) 159-179. Zbl0952.35042MR1635912
12. [12] Lin S.S., Asymptotic behavior of positive solutions to semilinear elliptic equations on expanding annuli, J. Differential Equations120 (2) (1995) 255-288. Zbl0839.35039MR1347346
13. [13] Pohozaev S., Eingenfunctions of the equation Δu+λfu=0, Soviet Math. Dokl.6 (1965) 1408-1411. Zbl0141.30202
14. [14] Rey O., The role of Green's function in a nonlinear elliptic equation involving critical Sobolev exponent, J. Funct. Anal.89 (1990) 1-52. Zbl0786.35059MR1040954
15. [15] Struwe M., Variational Methods: Applications to Nonlinear PDE & Hamiltonian Systems, Springer-Verlag, Berlin, 1990. Zbl0746.49010MR1078018

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