Uniqueness of positive bound states to schrödinger systems with critical exponents

SIAM Journal on Mathematical Analysis

Volumn 40, Issue 3, 2008, Pages 1049-1057

  Li, Congming ^a   Ma, Li ^b  

^a UNIVERSITY OF COLORADO   (United States)

^b TSINGHUA UNIVERSITY   (China)

Author keywords

Moving plane; Positive solutions; Radial symmetric; Uniqueness

Indexed keywords

BOSE-EINSTEIN CONDENSATES; BOUND STATE; CRITICAL EXPONENT; ELLIPTIC SYSTEM; KEYPOINTS; MOVING PLANE; POSITIVE SOLUTION; POSITIVE SOLUTIONS; RADIAL SYMMETRIC; RADIAL SYMMETRY; UNIQUENESS;

STEAM CONDENSERS;

BOSE-EINSTEIN CONDENSATION;

EID: 67650079024     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/080712301     Document Type: Article

References (28)

1. J. BOURGAIN, Global Solutions of Nonlinear Schrödinger Equations, Amer. Math. Soc. Colloq. Publ. 46, AMS, Providence, RI, 1999.
2. L. CAFFARELLI, B. GIDAS, AND J. SPRUCK, Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth, Comm. Pure Appl. Math., 42 (1989), pp. 271-297.
3. W. CHEN AND C. Li, Classification of solutions of some nonlinear elliptic equations, Duke Math. J., 63 (1991), pp. 615-622.
4. W. CHEN AND C. LI, Regularity of solutions for a system of integral equations, Comm. Pure Appl. Anal., 4 (2005), pp. 1-8.
5. W. CHEN AND C. LI, The best constant in weighted Hardy-Littlewood-Sobolev inequality, Proc. Amer. Math. Soc., 136 (2008), pp. 955-962.
6. W. CHEN, C. LI, AND B. OU, Classification of solutions for a system of integral equations, Comm. Partial Differential Equations, 30 (2005), pp. 59-65.
7. W. CHEN, C. LI, AND B. OU, Qualitative properties of solutions for an integral equation, Discrete Contin. Dyn. Syst., 12 (2005), pp. 347-354.
8. W. CHEN, C. Li, AND B. OU, Classification of solutions for an integral equation, Comm. Pure Appl. Math., 59 (2006), pp. 330-343.
9. D. G. DE FIGUEIREDO AND P. L. FELMER, On superquadratic elliptic systems, Trans. Amer. Math. Soc., 343 (1994), pp. 99-116.
10. D. G. DE FIGUEIREDO AND P. L. FELMER, A Liouville-type theorem for elliptic systems, Ann. Sc. Norm. Super. Pisa Cl. Sci. (4), 21 (1994), pp. 387-397.
11. n, in Mathematical Analysis and Applications, Part A, Adv. Math. Suppl. Stud. 7A, Academic Press, New York, 1981, pp. 369-402.
12. F. B. HANG, On the integral systems related to Hardy-Littlewood-Sobolev inequality, Math. Res. Lett., 14 (2007), pp. 373-383.
13. C. JIN AND C. LI, Symmetry of solutions to some integral equations, Proc. Amer. Math. Soc., 134 (2006), pp. 1661-1670.
14. C. JIN AND C. Li, Quantitative analysis of some system of integral equations, Calc. Var. Partial Differential Equations, 26 (2006), pp. 447-457.
15. T. KANNA AND M. LAKSHMANAN, Exact soliton solutions, shape changing collisions, and partially coherent solitons in coupled nonlinear Schrödinger equations, Phys. Rev. Lett., 86 (2001), pp. 5043-5046.
16. C. LI, Local asymptotic symmetry of singular solutions to nonlinear elliptic equations, Invent. Math., 123 (1996), pp. 221-231.
17. C. LI AND J. LIM, The singularity analysis of solutions to some integral equations, Commun. Pure Appl. Anal., 6 (2007), pp. 453-464.
18. E. LIEB, Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities, Ann. of Math., 118 (1983), pp. 349-374.
19. n, n ≤ 3, Commun. Math. Phys., 255 (2005), pp. 629-653.
20. T. C. LIN AND J. WEI, Spikes in two coupled nonlinear Schrödinger equations, Ann. Inst. H. Poincaré Anal. Non Linéaire, 22 (2005), pp. 403-439.
21. L. MA AND D. Z. CHEN, A Liouville type theorem for an integral system, Comm. Pure Appl. Anal., 5 (2006), pp. 855-859.
22. L. MA AND D. Z. CHEN, Radial symmetry and monotonicity for an integral equation, J. Math. Anal. Appl., 342 (2008), pp. 943-949.
23. L. MA AND L. ZHAO, Sharp thresholds of blow up and global existence for the coupled nonlinear Schrödinger system, J. Math. Phys., 49 (2008), article 062103.
24. M. NAITO AND H. USAMI, Existence of nonoscillatory solutions to second-order elliptic systems of Emden-Fowler type, Indiana Univ. Math. J., 55 (2006), pp. 317-339.
25. J. SERRIN AND H. ZOU, Non-existence of positive solutions of Lane-Emden systems, Differential Integral Equations, 9 (1996), pp. 635-653.
26. E. M. STEIN AND G. WEISS, Fractional integrals in n-dimensional Euclidean space, J. Math. Mech., 7 (1958), pp. 503-514.
27. J. WEI AND X. Xu, Classification of solutions of higher order conformally invariant equations, Math. Ann., 313 (1999), pp. 207-228.
28. M. I. WEINSTEIN, Nonlinear Schrödinger equations and sharp interpolate estimates, Comm. Math. Phys., 87 (1983), pp. 567-576.