Exotic solutions of the conformal scalar curvature equation in Rn

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1. [1] Bahri A, Coron J, The scalar-curvature problem on standard three-dimensional sphere, J. Func. Anal.95 (1991) 106-172. Zbl0722.53032MR1087949
2. [2] 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
3. [3] Chang K.-C, Liu J.-Q, On Nirenberg's problem, Internat. J. Math.4 (1993) 35-58. Zbl0786.58010MR1209959
4. [4] Chang S.-Y, Yang P, A perturbation result in prescribing scalar curvature on Sn, Duke Math. J.64 (1991) 27-69. Zbl0739.53027MR1131392
5. [5] Chen C.-C, Lin C.-S, On compactness and completeness of conformal metrics in RN, Asian J. Math.1 (1997) 549-559. Zbl0901.53027MR1604918
6. [6] Chen C.-C, Lin C.-S, Estimates of the conformal scalar curvature equation via the method of moving planes, Comm. Pure Appl. Math.50 (1997) 971-1019. Zbl0958.35013MR1466584
7. [7] Chen C.-C, Lin C.-S, Estimates of the conformal scalar curvature equation via the method of moving planes. II, J. Differential Geom.49 (1998) 115-178. Zbl0961.35047MR1642113
8. [8] Chen C.-C, Lin C.-S, On the asymptotic symmetry of singular solutions of the scalar curvature equations, Math. Ann.313 (1999) 229-245. Zbl0927.35034MR1679784
9. [9] Chen W.-X, Li C.-M, A necessary and sufficient condition for the Nirenberg problem, Comm. Pure Appl. Math.48 (1995) 657-667. Zbl0830.35034MR1338474
10. [10] Cheung K.-L, Leung M.-C, Asymptotic behavior of positive solutions of the equation Δu+Ku(n+2)/(n−2)=0 in Rn and positive scalar curvature, in: Discrete Contin. Dynam. Systems, Added Volume, Proceedings of the International Conference on Dynamical Systems and Differential Equations, 2001, pp. 109-120. 
11. [11] Delaunay C, Sur la surface de revolution dont la courbure moyenne est constante, J. de Mathématiques6 (1841) 309-320. 
12. [12] Ding W.-Y, Ni W.-M, On the elliptic equation Δu+Ku(n+2)/(n−2)=0 and related topics, Duke Math. J.52 (1985) 485-506. Zbl0592.35048
13. [13] Fowler R, Further studies of Emden's and similar differential equations, Quart. J. Math. Oxford Ser.2 (1931) 259-288. Zbl0003.23502
14. [14] Gidas B, Ni W.-M, Nirenberg L, Symmetry and related properties via the maximum principle, Comm. Math. Phys.68 (1979) 209-243. Zbl0425.35020MR544879
15. [15] Gidas B, Ni W.-M, Nirenberg L, Symmetry of positive solutions of nonlinear elliptic equations in Rn, in: Mathematical Analysis and Applications, Part A, Adv. in Math. Suppl. Stud., 7a, Academic Press, New York, 1981, pp. 369-402. Zbl0469.35052MR634248
16. [16] Korevaar N, Mazzeo R, Pacard F, Schoen R, Refined asymptotics for constant scalar curvature metrics with isolated singularities, Invent. Math.135 (1999) 233-272. Zbl0958.53032MR1666838
17. [17] Leung M.-C, Conformal scalar curvature equations on complete manifolds, Comm. Partial Differential Equations20 (1995) 367-417. Zbl0833.53038MR1318076
18. [18] Leung M.-C, Asymptotic behavior of positive solutions of the equation Δgu+Kup=0 in a complete Riemannian manifold and positive scalar curvature, Comm. Partial Differential Equations24 (1999) 425-462. Zbl0939.58024
19. [19] Leung M.-C., Growth estimates on positive solutions of the equation Δu+Ku(n+2)/(n−2)=0 in Rn, Canad. Math. Bull., to appear. Zbl0979.35046
20. [20] Li Y.-Y, Prescribing scalar curvature on Sn and related problems, part I, J. Differential Equations120 (1995) 319-410. Zbl0827.53039MR1347349
21. [21] Li Y.-Y, Prescribing scalar curvature on Sn and related problems, part II: existence and compactness, Comm. Pure Appl. Math.49 (1996) 541-597. Zbl0849.53031MR1383201
22. [22] Lin C.-S, Estimates of the conformal scalar curvature equation via the method of moving planes III, Comm. Pure Appl. Math.53 (2000) 611-646. Zbl1035.53052MR1737506
23. [23] Loewner C, Nirenberg L, Partial differential equations invariant under conformal or projective transformations, in: Contributions to Analysis (a collection of papers dedicated to Lipman Bers), Academic Press, New York, 1974, pp. 245-272. Zbl0298.35018MR358078
24. [24] Mazzeo R, Pacard F, Constant scalar curvature metrics with isolated singularities, Duke Math. J.99 (1999) 353-418. Zbl0945.53024MR1712628
25. [25] Mazzeo R, Pollack D, Uhlenbeck K, Moduli spaces of singular Yamabe metrics, J. Amer. Math. Soc.9 (1996) 303-344. Zbl0849.58012MR1356375
26. [26] Schoen R, The existence of weak solutions with prescribed singular behavior for a conformally invariant scalar equation, Comm. Pure Appl. Math.41 (1988) 317-392. Zbl0674.35027MR929283
27. [27] Taliaferro S, On the growth of superharmonic functions near an isolated singularity, I., J. Differential Equations158 (1999) 28-47. Zbl0939.31005MR1721720