Stability results for some nonlinear elliptic equations involving the $p$-laplacian with critical Sobolev growth

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1. [1] T. Aubin, Problèmes isopérimétriques et espaces de Sobolev. J. Differential Geom. 11 ( 1976) 573-598. Zbl0371.46011MR448404
2. [2] T. Aubin, Nonlinear Analysis on Manifolds. Monge-Ampere equations, Springer-Verlag ( 1982) (Grundlehren) 252. Zbl0512.53044MR681859
3. [3] O. Druet, Generalized scalar curvature type equations on compact riemaniann manifolds. Preprint of the University of Cergy-Pontoise ( 1997). MR1649975
4. [4] F. Demengel and E. Hebey, On some nonlinear equations involving the p-Laplacian with critical Sobolev growth. Adv. in PDE's, to appear. Zbl0955.35031MR1659246
5. [5] P. Courilleau and F. Demengel, On the heat flow for p-harmonic maps with values in S1. Nonlinear Anal. TMA, accepted. Zbl0979.35082
6. [6] M. Guedda and L. Veron, Local and global properties of solutions of quasilinear elliptic equations. J. Differential Equations 76 ( 1988) 159-189. Zbl0661.35029MR964617
7. [7] M. Guedda and L. Veron, Quasilinear elliptic equations involving critical Sobolev exponentsNonlinear Analysis, Theory, Methods and Applications 13 ( 1989) 879-902. Zbl0714.35032MR1009077
8. [8] E. Hebey and M. Vaugon, Existence and multiplicity of nodal solutions for nonlinear elliptic equations with critical Sobolev growth. J. Funct. Anal. 119 ( 1994) 298-318. Zbl0798.35052MR1261094
9. [9] L.C. Evans, Weak convergence methods for nonlinear partial differential equations. Conference Board of the Mathematical Sciences 74 ( 1990). Zbl0698.35004MR1034481
10. [10] E. Hebey, La methode d'isométries-concentration dans le cas d'un problème non linéaire sur les variétés compactes à bord avec exposant critique de sobolev. Bull. Sci. Math. 116 ( 1992) 35-51. Zbl0756.35028MR1154371
11. [11] E. Hebey, Sobolev Spaces on Riemannian Manifolds, Springer-Verlag ( 1996) (LNM) 1635. Zbl0866.58068MR1481970
12. [12] A. Jourdain, Solutions nodales pour des équations de type courbure scalaire sur la sphère. Preprint of the University of Cergy-Pontoise ( 1997). 
13. [13] P.L. Lions, The concentration-compactness principle in the calculus of variations. The limit case, part I. Revista Matematica Iberoamericana 1 ( 1985) 145-199. Zbl0704.49005MR834360
14. [14] P.L. Lions, The concentration-compactness principle in the calculus of variations. The limit case, part II. Revista Matematica Iberoamericana 1 ( 1985) 45-116. Zbl0704.49006MR850686
15. [15] B. Nazaret, Stabilité sous des perturbations visqueuses des solutions d'équations du type p-Laplacien avec exposant critique de Sobolev. Preprint of the University of Cergy-Pontoise (5/98). 
16. [16] G. Talenti. Best constants in Sobolev inequalities. Ann. Mat. Pura Appl. 110 ( 1976) 353-372. Zbl0353.46018MR463908
17. [17] P. Tolksdorf, Regularity for a more general class of quasilinear elliptic equations. J. Differential Equations 51 ( 1984) 126-150. Zbl0488.35017MR727034
18. [18] J.L. Vazquez, A strong maximum principle for some quasilinear elliptic equations. Appl. Math. Optim. 12 ( 1984) 191-202. Zbl0561.35003MR768629