Existence of infinitely many solutions for the (p,q)-Laplace equation

被引：11
|
作者：
Komiya, Yukinori [1 ]
Kajikiya, Ryuji [2 ]
机构：
[1] Saga Univ, Grad Sch Sci & Engn, Saga 8408502, Japan
[2] Saga Univ, Dept Math, Fac Sci & Engn, Saga 8408502, Japan
来源：
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2016年 / 23卷 / 04期
关键词：
(p; q)-Laplace equation; superlinear; sublinear; infinitely many solutions; a priori estimate; variational method; Q ELLIPTIC PROBLEMS; Q-LAPLACIAN TYPE; NONTRIVIAL SOLUTION; POSITIVE SOLUTIONS; CONVEX NONLINEARITIES; CRITICAL EXPONENT; Q)-LAPLACIAN; (P; MULTIPLICITY; CONCAVE;
D O I：
10.1007/s00030-016-0402-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study the (p,q)-Laplace equation in a bounded domain under the Dirichlet boundary condition. We give a sufficient condition of the nonlinear term for the existence of a sequence of solutions converging to zero or diverging to infinity. Moreover, we give a priori estimates of the C-1-norms of solutions under a suitable condition on the nonlinear term.
引用
收藏
页数：23
相关论文
共 50 条
  • [1] Existence of infinitely many solutions for the (p, q)-Laplace equation
    Yukinori Komiya
    Ryuji Kajikiya
    Nonlinear Differential Equations and Applications NoDEA, 2016, 23
  • [2] Existence of Infinitely Many Solutions for Δγ-Laplace Problems
    Luyen, D. T.
    Huong, D. T.
    Hanh, L. T. H.
    MATHEMATICAL NOTES, 2018, 103 (5-6) : 724 - 736
  • [3] Existence of Infinitely Many Solutions for Δγ-Laplace Problems
    D. T. Luyen
    D. T. Huong
    L. T. H. Hanh
    Mathematical Notes, 2018, 103 : 724 - 736
  • [4] Infinitely many solutions for quasilinear elliptic equations involving (p, q)-Laplacian in R
    Teng, Kaimin
    Zhang, Chao
    NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2016, 32 : 242 - 259
  • [5] Existence of infinitely many solutions for a Steklov problem involving the p(x)-Laplace operator
    Allaoui, Mostafa
    El Amrouss, Abdel Rachid
    Ourraoui, Anass
    ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2014, (20) : 1 - 10
  • [6] On the existence of infinitely many solutions of a nonlinear Neumann problem involving the m-Laplace operator
    Stancut, Ionela-Loredana
    ANNALS OF THE UNIVERSITY OF CRAIOVA-MATHEMATICS AND COMPUTER SCIENCE SERIES, 2015, 42 (02): : 402 - 426
  • [7] Existence of infinitely many solutions for a quasilinear elliptic equation
    Zhang, Jian
    Tang, Xianhua
    Zhang, Wen
    APPLIED MATHEMATICS LETTERS, 2014, 37 : 131 - 135
  • [8] Infinitely many solutions for fourth-order semilinear Δγ - Laplace equation in RN
    Duong Trong Luyen
    Ninh Tien Nam
    JOURNAL OF ELLIPTIC AND PARABOLIC EQUATIONS, 2021, 7 (02) : 977 - 988
  • [9] Infinitely many periodic solutions for second-order (p, q)-Laplacian differential systems
    Li, Yongkun
    Zhang, Tianwei
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (15) : 5215 - 5221
  • [10] Existence of solutions for the (p, q)-Laplacian equation with nonlocal Choquard reaction
    Xie, Xiaoliang
    Wang, Tianfang
    Zhang, Wen
    APPLIED MATHEMATICS LETTERS, 2023, 135
12345