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一类拟线性Schrdinger方程非平凡解的存在性 被引量：6

Existence of Nontrivial Solution for a Class of Quasilinear Schrdinger Equations
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摘要 在没有(AR)条件的情况下,利用山路引理和Lions引理,通过变量替换,得到一类拟线性Schrdinger方程非平凡解的存在性. The existence of nontrivial solution for a class of quasilinear Schrodinger equation is established by variable substitution, based on the mountain pass lemma and Lions lemma, without （AR） condition.
作者 刘西洋 商彦英 唐春雷
机构地区 西南大学数学与统计学院
出处 《西南大学学报（自然科学版）》 CAS CSCD 北大核心 2014年第2期77-81,共5页 Journal of Southwest University(Natural Science Edition)
基金 国家自然科学基金资助项目(11071198)
关键词 拟线性Schrdinger方程 存在性 非平凡解 quasilinear SchrOdinger equation existence nontrivial solution
分类号 O413.1 [理学—理论物理]
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参考文献6

  • 1KELLEYP L. Self Focusing of Optical Beams [J]. Phys Rev Lett, 1965, 15(26): 1005-1008.
  • 2POPPENBERG M, SCHMIT K, WANG Zhi-qiang. On the Existence of Soliton Solutions to Quasilinear Schr{3dinger E- quations [J]. Calc Var Partial Differential Equations, 2002, 14(3): 329-344.
  • 3LIU Jia-quan, WANG Zhi-qiang. Soliton Solutions for Quasilinear Schr6dinger Equations II [J]. J Differential Equa tions, 2003, 187(2): 473-493.
  • 4LIU Xiang-qing, LIU Jia quan, WANG Zhi-qiang. Quasilinear Elliptic Equations Via Perturbation Method [J]. Proc A mer Math Soc, 2013, 141(1) : 253-263.
  • 5SHEN Yao-tian, WANG You jun. Soliton Solutions for Generalized Quasilinear Schr6dinger Equations EJ:. Nonlinear Analysis, 2013, 80: 194-201.
  • 6LIONS P L. The Concentration-Compactness Principle in the Calculus of Variations: The Locally Compact Case [J]. Ann Inst Poincarfi Anal Non Lin6aire, 1984, 1(2): 109-145.

同被引文献42

  • 1LAZER A C, MCKENNA P J. On a Singular Nonlinear Elliptic Boundary-Value Problem [J]. Proc Amer Math Soc, 1991, 111(3): 721-730.
  • 2SUN Yi-jing, WU Shao-ping, LONG Yi-ming. Combined Effects of Singular and Superlinear Nonlinearities in Some Sin- gular Boundary Value Problems [J]. J Differential Equations, 2001, 176: 511-531.
  • 3SUN Yi-jing, WU Shao-ping. An Exact Estimate Result for a Class of Singular Equations with Critical Exponents [J]. J Funct Anal, 2011, 260: 1257-1284.
  • 4CHABROWSKI J. On the Neumann Problem with Singular and Superlinear Nonlinearities [J]. Commun Appl Anal, 2009, 13(3): 327-339.
  • 5LIAO Jia-feng, LIU Jiu, TANG Chun-lei, et al. Existence of Two Positive Solutions for a Singular Neumann Problem [J]. Electronic Journal of Differential Equations, 2014, 84 : 1- 17.
  • 6RUDIN W. Real and Complex Analysis [M]. New York: McGraw-Hill Science, 1966.
  • 7David Ruiz.The Schr?dinger–Poisson equation under the effect of a nonlinear local term[J]. Journal of Functional Analysis . 2006 (2)
  • 8Francisco Odair de Paiva,Adilson E. Presoto.Semilinear elliptic problems with asymmetric nonlinearities[J]. Journal of Mathematical Analysis and Applications . 2013
  • 9Yang Yang,Jihui Zhang.Positive and negative solutions of a class of nonlocal problems[J]. Nonlinear Analysis . 2010 (1)
  • 10Zhitao Zhang,Kanishka Perera.Sign changing solutions of Kirchhoff type problems via invariant sets of descent flow[J]. Journal of Mathematical Analysis and Applications . 2005 (2)

引证文献6

二级引证文献18

西南大学学报（自然科学版）
2014年 第2期

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