Eigenvalues of -Δp - Δq Under Neumann Boundary Condition

被引:9
|
作者
Mihailescu, Mihai [1 ,2 ]
Morosanu, Gheorghe [3 ]
机构
[1] Univ Craiova, Dept Math, Craiova 200585, Romania
[2] Romanian Acad, Simion Stoilow Inst Math, Res Grp, Project PN II ID PCE 2012 4 0021, Bucharest 010702, Romania
[3] Cent European Univ, Dept Math & Its Applicat, H-1051 Budapest, Hungary
关键词
eigenvalue problem; Sobolev space; Nehari manifold; variational methods;
D O I
10.4153/CMB-2016-025-2
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
The eigenvalue problem -Delta(p)u - Delta(q)u = lambda vertical bar u vertical bar(q-2)u with p is an element of (1, infinity), q is an element of (2, infinity), p not equal q subject to the corresponding homogeneous Neumann boundary condition is investigated on a bounded open set with smooth boundary from R-N with N >= 2. A careful analysis of this problem leads us to a complete description of the set of eigenvalues as being a precise interval (lambda(1), +infinity) plus an isolated point lambda = 0. This comprehensive result is strongly related to our framework, which is complementary to the well-known case p = q not equal 2 for which a full description of the set of eigenvalues is still unavailable.
引用
收藏
页码:606 / 616
页数:11
相关论文
共 50 条
  • [21] EIGENVALUES OF THE LAPLACIAN WITH NEUMANN BOUNDARY-CONDITIONS
    GOTTLIEB, HPW
    [J]. JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES B-APPLIED MATHEMATICS, 1985, 26 (JAN): : 293 - 309
  • [22] Landesman-Lazer type (p, q)-equations with Neumann condition
    Nikolaos S. Papageorgiou
    Calogero Vetro
    Francesca Vetro
    [J]. Acta Mathematica Scientia, 2020, 40 : 991 - 1000
  • [23] Landesman-Lazer type (p, q)-equations with Neumann condition
    Papageorgiou, Nikolaos S.
    Vetro, Calogero
    Vetro, Francesca
    [J]. ACTA MATHEMATICA SCIENTIA, 2020, 40 (04) : 991 - 1000
  • [24] LANDESMAN-LAZER TYPE(p, q)-EQUATIONS WITH NEUMANN CONDITION
    Nikolaos S.PAPAGEORGIOU
    Calogero VETRO
    Francesca VETRO
    [J]. Acta Mathematica Scientia, 2020, 40 (04) : 991 - 1000
  • [25] Estimates of solutions of impulsive parabolic equations under Neumann boundary condition
    Gao, WL
    Wang, JH
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2003, 283 (02) : 478 - 490
  • [26] RESONANT (p,q)-EQUATIONS WITH ROBIN BOUNDARY CONDITION
    Filippakis, Michael E.
    Papageorgiou, Nikolaos S.
    [J]. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2018,
  • [27] Lyapunov inequalities for Neumann boundary conditions at higher eigenvalues
    Canada, A.
    Villegas, S.
    [J]. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2010, 12 (01) : 163 - 178
  • [28] Roughness effect on Neumann boundary condition
    Chupin, Laurent
    [J]. ASYMPTOTIC ANALYSIS, 2012, 78 (1-2) : 85 - 121
  • [29] Principal Eigenvalues for Isaacs Operators with Neumann Boundary Conditions
    Stefania Patrizi
    [J]. Nonlinear Differential Equations and Applications NoDEA, 2009, 16 : 79 - 107
  • [30] Principal Eigenvalues for Isaacs Operators with Neumann Boundary Conditions
    Patrizi, Stefania
    [J]. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2009, 16 (01): : 79 - 107