- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 504282, 5 pages
Necessary Conditions for Existence Results of Some Integral System
1Center of Applied Math, Harbin Institute of Technology, Shenzhen Graduate School, Shenzhen, Guangdong 518055, China
2Institute for Advanced Study, Shenzhen University, Shenzhen, Guangdong 518060, China
Received 3 May 2013; Accepted 13 July 2013
Academic Editor: Jaume Giné
Copyright © 2013 Yongxia Hua and Xiaohui Yu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- E. H. Lieb, “Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities,” Annals of Mathematics. Second Series, vol. 118, no. 2, pp. 349–374, 1983.
- W. Chen, C. Li, and B. Ou, “Classification of solutions for an integral equation,” Communications on Pure and Applied Mathematics, vol. 59, no. 3, pp. 330–343, 2006.
- W. Chen, C. Li, and B. Ou, “Classification of solutions for a system of integral equations,” Communications in Partial Differential Equations, vol. 30, no. 1–3, pp. 59–65, 2005.
- Y. Y. Li, “Remark on some conformally invariant integral equations: the method of moving spheres,” Journal of the European Mathematical Society, vol. 6, no. 2, pp. 153–180, 2004.
- X. Yu, “Liouville type theorems for integral equations and integral systems,” Calculus of Variations and Partial Differential Equations, vol. 46, no. 1-2, pp. 75–95, 2013.
- X. Yu, “Liouville type theorems for singular integral equations and integral systems,” Calculus of Variations and Partial Differential Equations, vol. 46, no. 1-2, pp. 75–95, 2013.
- W. Chen and C. Li, “An integral system and the Lane-Emden conjecture,” Discrete and Continuous Dynamical Systems. Series A, vol. 24, no. 4, pp. 1167–1184, 2009.
- W. Chen and C. Li, “Classification of positive solutions for nonlinear differential and integral systems with critical exponents,” Acta Mathematica Scientia. Series B. English Edition, vol. 29, no. 4, pp. 949–960, 2009.
- W. Chen and C. Li, Methods on Nonlinear Elliptic Equations, vol. 4 of AIMS Series on Differential Equations & Dynamical Systems, American Institute of Mathematical Sciences, Springfield, Mo, USA, 2010.
- W. Chen and C. Li, “Radial symmetry of solutions for some integral systems of Wolff type,” Discrete and Continuous Dynamical Systems. Series A, vol. 30, no. 4, pp. 1083–1093, 2011.
- F. Hang, X. Wang, and X. Yan, “An integral equation in conformal geometry,” Annales de l'Institut Henri Poincaré. Analyse Non Linéaire, vol. 26, no. 1, pp. 1–21, 2009.
- C. Jin and C. Li, “Symmetry of solutions to some systems of integral equations,” Proceedings of the American Mathematical Society, vol. 134, no. 6, pp. 1661–1670, 2006.
- L. Ma and D. Chen, “A Liouville type theorem for an integral system,” Communications on Pure and Applied Analysis, vol. 5, no. 4, pp. 855–859, 2006.
- L. Ma and D. Chen, “Radial symmetry and monotonicity for an integral equation,” Journal of Mathematical Analysis and Applications, vol. 342, no. 2, pp. 943–949, 2008.
- L. Ma and D. Chen, “Radial symmetry and uniqueness for positive solutions of a Schrödinger type system,” Mathematical and Computer Modelling, vol. 49, no. 1-2, pp. 379–385, 2009.
- C. Ma, W. Chen, and C. Li, “Regularity of solutions for an integral system of Wolff type,” Advances in Mathematics, vol. 226, no. 3, pp. 2676–2699, 2011.
- X. Xu, “Exact solutions of nonlinear conformally invariant integral equations in ,” Advances in Mathematics, vol. 194, no. 2, pp. 485–503, 2005.
- X. Xu, “Uniqueness and non-existence theorems for conformally invariant equations,” Journal of Functional Analysis, vol. 222, no. 1, pp. 1–28, 2005.
- X. Xu, “Uniqueness theorem for integral equations and its application,” Journal of Functional Analysis, vol. 247, no. 1, pp. 95–109, 2007.
- W. P. Ziemer, Weakly Differentiable Functions. Sobolev Spaces and Functions of Bounded Variation, vol. 120 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 1989.