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Liouville-Type Theorems for Some Integral Systems
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Abstract
In this paper, Liouville-type theorems of nonnegative solutions for some elliptic integral systems are considered. We use a new type of moving plane method introduced by Chen-Li-Ou. Our new ingredient is the use of Stein-Weiss inequality instead of Maximum Principle.
KeywordsLiouville TheoremIntegral SystemMoving Plane Method
- W. X. Chen and C. M. Li, “Classification of Positive Solutions for Nonlinear Differential and Integral Systems with Critical Exponents,” Acta Mathematica Scientia, in press.
- W. X. Chen, C. M. Li and B. Ou, “Classification of Solutions for an Integral Equation,” Communications on Pure and Applied Mathematics, Vol. 59, No. 3, 2006, pp. 330- 343.
- L. Caffarelli, B. Gidas and J. Spruck, “Asymptotic Symmetry and Local Behavior of Semilinear Elliptic Equations with Critical Sobolev Growth,” Communications on Pure and Applied Mathematics, Vol. 42, No. 3, 1989, pp. 271-297.
- B. Gidas and J. Spruck, “Global and Local Behaviour of Positive Solutions of Nonlinear Elliptic Equations,” Communications on Pure and Applied Mathematics, Vol. 34, No. 6, 1981, pp. 525-598.
- S. H. Chen and G. Z. Lu, “Existence and Nonexistence of Positive Radial Solutions for a Class of Semilinear Elliptic System,” Nonlinear Analysis, Vol. 38, No. 7, 1999, pp. 919-932.
- E. Mitidieri, “Nonexistence of Positive Solutions of Semilinear Elliptic Systems in ,” Differential and Integral Equations, Vol. 9, No. 3, 1996, pp. 465-479.
- E. Lieb, “Sharp Constants in the Hardy-Littlewood- Sobolev and Related Inequalities,” Annals of Mathematics, Vol. 118, 1983, pp. 349-374.
- D. G. de Figueiredo and P. L. Felmer, “A Liouville-Type Theorem for Elliptic Systems,” Annali della Scuola Normale Superiore di Pisa XXI, Vol. 21, No. 3, 1994, pp. 387-397.
- J. Busca and R. Manásevich, “A Liouville-Type Theorem for Lane-Emden Systems,” Indiana University Mathematics Journal, Vol. 51, No. 1, 2002, pp. 37-51.
- Z. C. Zhang, W. M. Wang and K. T. Li, “Liouville-Type Theorems for Semilinear Elliptic Systems,” Journal of Partial Differential Equations, Vol. 18, No. 4, 2005, pp. 304-310.
- Y. Y. Li and M. Zhu, “Uniqueness Theorems through the Method of Moving Spheres,” Duke Mathematical Journal, Vol. 80, No. 2, 1995, pp. 383-417.
- Y. Y. Li and L. Zhang, “Liouville-Type Theorems and Harnack-Type Inequalities for Semilinear Elliptic Equations,” Journal d’Analyse Mathematique, Vol. 90, 2003, pp. 27-87.
- W. X. Chen, C. M. Li and B. Ou, “Classification of Solutions for a System of Integral Equations,” Communications in Partial Differential Equations, Vol. 30, No. 1-2, 2005, pp. 59-65.
- W. X. Chen, C. M. Li and B. Ou, “Qualitative Properties of Solutions for an Integral Equation,” Discrete and Continuous Dynamical Systems, Vol. 12, No. 2, 2005, pp. 347-354.