带有非自治项的非线性Schrödinger方程的基态解的存在性
Ground States of Nonlinear Schrödinger Equation with Non-Autonomous Nonlinearity
DOI: 10.12677/pm.2012.22011, PDF, HTML,  被引量    国家自然科学基金支持
作者: 朱红波：广东工业大学应用数学学院
关键词: 非线性Schrödinger方程；基态解；集中紧致原理；Nonlinear Schrödinger Equation; Ground State Solutions; Concentration Compactness
摘要: 本文考虑如下形式的非线性Schrödinger方程 (P)。利用有界区域逼近和集中紧致原理，当位势函数不恒等于常数，非线性项 不恒等于 ，本文证明了方程(P)存在最低能量解。
Abstract: In this paper, we are concerned with the following nonlinear Schrödinger equation (P). By using the bounded domain approximate scheme and concen-tration compactness principle, we prove the existence of a ground state solution of (P) on the Nehari manifold when constant and .
文章引用：朱红波. 带有非自治项的非线性Schrödinger方程的基态解的存在性[J]. 理论数学, 2012, 2(2): 62-72. http://dx.doi.org/10.12677/pm.2012.22011

参考文献

[1] L. Jeanjean. On the existence of bounded Palais-Smale sequence and application to a Landesman-Lazer-type problem set on RN. Proceedings of the Royal Society of Edinburgh, 1999, 129(4): 787-809.
[2] L. Jeanjean, K, Tanaka. A positive solution for an asymptotically linear elliptic problem on RN autonomous at infinity. ESAIM Control Optimisation and Calcules of Variations, 2002, 7: 597-614.
[3] L. Jeanjean, K. Tanaka. A positive solution for a linear Schrödinger equation on RN. Indiana University Mathematics Journal, 2005, 54(2): 443-464.
[4] C. Y. Liu, Z. P. Wang and H. S. Zhou. Asymptotically of nonlinear Schrödinger equation with potential vanishing at infinity. Journal of Differential Equations, 2008, 245(1): 201-222.
[5] G. Li, H. S. Zhou. The existence of a positive solution to asymptotically linear scalar field equation. Proceedings of the Royal Societyof Edinburgh, 2000, 130(1): 81-105.
[6] H. B. Zhu. A note on asymptotically linear Schrödinger equation on RN. Advanced Nonlinear Studies, 2009, 9(1): 81-94.
[7] A. Ambrosetti, P. H. Rabinowitz. Dual variational methods in critical point theory and application. Journal of Functional Analysis, 1973, 14(4): 349-381.
[8] Z. L. Liu, Z. Q. Wang. On the Ambrosetti-Rabinowitz superlinear condition. Advanced Nonlinear Studies, 2004, 4(4): 561-572.
[9] Y. Q. Li, Z. Q. Wang and J. Zeng. Ground states of nonlinear Schrödinger equations with potentials. Annales de I’Institut Henri Poincare, 2006, 23(6): 829-837.
[10] M. Willem. Minimax theorems. Boston: Birkhauser, 1996.
[11] X. P. Zhu, D. M. Cao. The concentration-compactness principle in nonlinear elliptic equations. Acta Mathematica Scientia, 1989, 9(3): 307-323.
[12] P. L. Lions. The concentration-compactness principle in the calculus of variation. The locally compact case, Part I and II. Annales de I’Institut Henri Poincare, 1984, 1(4): 109-145, 223-283.

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