POSITIVE SOLUTIONS FOR NONLINEAR FRACTIONAL LAPLACIAN PROBLEMS

被引：0
|
作者：
Hollifield, Elliott [1 ]
机构：
[1] Univ N Carolina, Pembroke, NC 28372 USA
来源：
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS | 2023年
关键词：
Fractional Laplacian; sublinear; asymptotically linear; sub- and supersolution; positive weak solution; EXTENSION PROBLEM;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider a class of nonlinear fractional Laplacian problems satisfying the homogeneous Dirichlet condition on the exterior of a bounded domain. We prove the existence of a positive weak solution for classes of nonlinearities which are either sublinear or asymptotically linear at infinity. We use the method of sub-and-supersolutions to establish the results. We also provide numerical bifurcation diagrams, corresponding to the theoretical results, using the finite element method in one dimension.
引用
收藏
页码：135 / 149
页数：15
相关论文
共 50 条
  • [21] Positive solutions for a system of nonlinear fractional nonlocal boundary value problems with parameters and p-Laplacian operator
    Xinan Hao
    Huaqing Wang
    Lishan Liu
    Yujun Cui
    Boundary Value Problems, 2017
  • [22] Positive solutions for a system of nonlinear fractional nonlocal boundary value problems with parameters and p-Laplacian operator
    Hao, Xinan
    Wang, Huaqing
    Liu, Lishan
    Cui, Yujun
    BOUNDARY VALUE PROBLEMS, 2017,
  • [23] Positive Solutions for Nonlinear Periodic Problems with the Scalar p-Laplacian
    Denkowski, Zdzislaw
    Gasinski, Leszek
    Papageorgiou, Nikolaos S.
    SET-VALUED ANALYSIS, 2008, 16 (5-6): : 539 - 561
  • [24] Positive Solutions for Nonlinear Periodic Problems with the Scalar p-Laplacian
    Zdzisław Denkowski
    Leszek Gasiński
    Nikolaos S. Papageorgiou
    Set-Valued Analysis, 2008, 16 : 539 - 561
  • [25] Nonexistence and Uniqueness of Positive Solutions to a Nonlinear Fractional p-Laplacian System
    Kong Xiangshan
    Li Haitao
    2013 32ND CHINESE CONTROL CONFERENCE (CCC), 2013, : 262 - 266
  • [26] Positive Solutions for Singular Superlinear φ-Laplacian Problems with Nonlinear Boundary Conditions
    Hai, D. D.
    Wang, X.
    MEDITERRANEAN JOURNAL OF MATHEMATICS, 2022, 19 (01)
  • [27] Symmetric positive solutions for nonlinear boundary value problems with φ-Laplacian operator
    Luo, Yan
    Luo, Zhiguo
    APPLIED MATHEMATICS LETTERS, 2010, 23 (06) : 657 - 664
  • [28] Multiple positive solutions for nonlinear eigenvalue problems with the p-Laplacian
    Hu, Shouchuan
    Papageorgiou, Nikolas S.
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 69 (12) : 4286 - 4300
  • [29] Positive solutions for nonlinear problems involving the one-dimensional φ-Laplacian
    Kaufmann, Uriel
    Milne, Leandro
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 461 (01) : 24 - 37
  • [30] Multiple positive solutions for nonlinear coupled fractional Laplacian system with critical exponent
    Zhen, Maoding
    He, Jinchun
    Xu, Haoyuan
    Yang, Meihua
    BOUNDARY VALUE PROBLEMS, 2018,
12345