Classification of positive solitary solutions of the nonlinear choquard equation

Archive for Rational Mechanics and Analysis

Volumn 195, Issue 2, 2009, Pages 455-467

  Ma, Li ^a   Zhao, Lin ^a  

^a TSINGHUA UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 72449193262     PISSN: 00039527     EISSN: 14320673     Source Type: Journal    
DOI: 10.1007/s00205-008-0208-3     Document Type: Article

References (24)

1. Adams R. A.: Sobolev Spaces. Academic Press, New York (1975).
2. Benguria R., Brezis H., Lieb E. H.: The Thomas-Fermi-von Weizsäcker theory of atoms and molecules. Comm. Math. Phys. 79, 167-180 (1981).
3. Cazenave T., Lions P. L.: Orbital stability of standing waves for some nonlinear Schrödinger equations. Comm. Math. Phys. 85, 549-561 (1982).
4. Chen W. X., Li C. M.: Classification of solutions of some nonlinear elliptic equations. Duke Math. J. 63, 615-622 (1991).
5. Chen W. X., Li C. M., Ou B.: Classification of solutions for an integral equation. Comm. Pure. Appl. Math. 59, 330-343 (2006).
6. Chen W. X., Li C. M., Ou B.: Classification of solutions for a system of integral equations. Comm. Partial Diff. Equations 30, 59-65 (2005).
7. Ginibre J., Velo G.: On a class of nonlinear Schrödinger equations with nonlocal interaction. Math. Z. 170, 109-136 (1980).
8. n. Mathematical Analysis and Appl. Academic Press, New York, 1981.
9. Gross, E. P.: Physics of Many-particle Systems, vol. 1. Gordon Breach, New York, 1996.
10. Jin C., Li C. M.: Symmetry of solutions to some systems of integral equations. Proc. Am. Math. Soc. 134, 1661-1670 (2005).
11. Li C. M., Ma L.: Uniqueness of positive bound states to Schrodinger systems with critical exponents. SIAM J. Math. Anal. 40(3), 1049-1057 (2008).
12. Lieb E. H.: Existence and uniqueness of the minimizing solution of Choquard's nonlinear equation. Stud. Appl. Math. 57, 93-105 (1977).
13. Lieb E. H.: Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities. Ann. Math. 118, 349-374 (1983).
14. Lieb E. H., Simon B.: The Hartree-Fock theory for Coulomb systems. Comm. Math. Phys. 53, 185-194 (1977).
15. Loins P. L.: The Choquard equation and related questions. Nonlinear Anal. T. M. A. 4, 1063-1073 (1980).
16. Lions, P. L.: Compactness and topological methods for some nonlinear variational problems of mathematical physics. Nonlinear Problems: Present and Future, pp. 17-34, 1982.
17. Lions P. L.: The concentration-compactness principle in the calculus of variations, The locally compact case, I and II. Ann. Inst. H. Poincaré., Anal. Nonlinéaire. 1(109-145), 223-283 (1984).
18. Ma L., Chen D. Z.: Radial syymetry and uniqueness result for an integral system. Math. Comput. Model. 49, 379-385 (2009).
19. Ma L., Chen D. Z.: Radial symmetry and monotonicity results for an integral equation. J. Math. Anal. Appl. 342, 943-949 (2008).
20. Ma L., Chen D. Z.: A Liouville type theorem for an integral system. Comm. Pure Appl. Anal. 5, 855-859 (2006).
21. Ma L., Zhao L.: Uniqueness of ground states of some coupled nonlinear Schrodinger systems and their application. J. Diff. Equ. 245, 2551-2565 (2008).
22. Rabinowitz P.: On a class of nonlinear Schrödinger equations. Z. Angew. Math. Phys. 43, 270-291 (1992).
23. Shatah J., Strauss W.: Instability of nonlinear bound states. Comm. Math. Phys. 100, 173-190 (1985).
24. Stein E. M.: Singular Integrals and Differentiability Properties of Functions. Princeton University Press, Princeton (1970).