On the Fuik spectrum of non-local elliptic operators

被引:15
作者
Goyal, Sarika [1 ]
Sreenadh, K. [1 ]
机构
[1] Indian Inst Technol Delhi, Dept Math, New Delhi 16, India
来源
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2014年 / 21卷 / 04期
关键词
Non-local operator; Fractional Laplacian; Fucik spectrum; Nonresonance; FUCIK SPECTRUM; P-LAPLACIAN;
D O I
10.1007/s00030-013-0258-6
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this article, we study the Fuik spectrum of the fractional Laplace operator which is defined as the set of all such that (-Delta)(s)u = alpha u(+) - beta u(-) in Omega u = 0 in R-n/Omega.} has a non-trivial solution u, where is a bounded domain in with Lipschitz boundary, n > 2s, . The existence of a first nontrivial curve of this spectrum, some properties of this curve , e.g. Lipschitz continuous, strictly decreasing and asymptotic behavior are studied in this article. A variational characterization of second eigenvalue of the fractional eigenvalue problem is also obtained. At the end, we study a nonresonance problem with respect to the Fuik spectrum.
引用
收藏
页码:567 / 588
页数:22
相关论文
共 24 条
  • [1] Alif M, 2002, LECT NOTES PURE APPL, V229, P45
  • [2] Ambrosetti A., 1973, Journal of Functional Analysis, V14, P349, DOI 10.1016/0022-1236(73)90051-7
  • [3] [Anonymous], 1982, ANN FAC SCI TOULOUSE
  • [4] RADIAL FUCIK SPECTRUM OF THE LAPLACE OPERATOR
    ARIAS, M
    CAMPOS, J
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1995, 190 (03) : 654 - 666
  • [5] A VARIATIONAL APPROACH TO NONRESONANCE WITH RESPECT TO THE FUCIK SPECTRUM
    CUESTA, M
    GOSSEZ, JP
    [J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1992, 19 (05) : 487 - 500
  • [6] The beginning of the Fucik spectrum for the p-Laplacian
    Cuesta, M
    de Figueiredo, D
    Gossez, JP
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1999, 159 (01) : 212 - 238
  • [7] Some remarks on the Fucik spectrum of the p-Laplacian and critical groups
    Dancer, EN
    Perera, K
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2001, 254 (01) : 164 - 177
  • [8] de Figueiredo DG., 1994, Differ Integr Equ, V7, P1285
  • [9] Hitchhiker's guide to the fractional Sobolev spaces
    Di Nezza, Eleonora
    Palatucci, Giampiero
    Valdinoci, Enrico
    [J]. BULLETIN DES SCIENCES MATHEMATIQUES, 2012, 136 (05): : 521 - 573
  • [10] Fucik S., 1980, Mathematics and Its Applications, V4