Existence of k-Convex Solutions for the k-Hessian Equation

被引：8
|
作者：
Bai, Zhanbing [1 ]
Yang, Zedong [1 ]
机构：
[1] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Shandong, Peoples R China
来源：
MEDITERRANEAN JOURNAL OF MATHEMATICS | 2023年 / 20卷 / 03期
基金：
中国国家自然科学基金;
关键词：
k-Hessian equation; existence; k-convex solution; cone; fixed point theorem; NONLINEAR GRADIENT TERMS; MONGE-AMPERE EQUATIONS; RADIAL SOLUTIONS; ELLIPTIC-EQUATIONS; SYSTEMS; NONEXISTENCE;
D O I：
10.1007/s00009-023-02364-8
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper considers the following Dirichlet boundary value problem of the k -Hessian equation: {S-k (sigma (D(2)z)) = lambda b(|x|)?(-z), in omega, z = 0, on & part;omega,where lambda > 0, omega stands for the open unit ball in R-N, 1 <= k <= N is an integer, and S-k (sigma (D(2)z)) is the k -Hessian operator of z. We obtain the existence results of k -convex radial solutions of the k -Hessian problem for lambda belonging to an open interval. Our main approach is the Guo- Krasnosel'skii fixed point theorem in a cone.
引用
收藏
页数：12
相关论文
共 50 条
  • [1] Existence of k-Convex Solutions for the k-Hessian Equation
    Zhanbing Bai
    Zedong Yang
    Mediterranean Journal of Mathematics, 2023, 20
  • [2] The existence and multiplicity of k-convex solutions for a coupled k-Hessian system
    Gao, Chenghua
    He, Xingyue
    Wang, Jingjing
    ACTA MATHEMATICA SCIENTIA, 2023, 43 (06) : 2615 - 2628
  • [3] THE EXISTENCE AND MULTIPLICITY OF k-CONVEX SOLUTIONS FOR A COUPLED k-HESSIAN SYSTEM
    高承华
    何兴玥
    王晶晶
    Acta Mathematica Scientia, 2023, 43 (06) : 2615 - 2628
  • [4] The existence and multiplicity of k-convex solutions for a coupled k-Hessian system
    Chenghua Gao
    Xingyue He
    Jingjing Wang
    Acta Mathematica Scientia, 2023, 43 : 2615 - 2628
  • [5] Multiplicity of k-convex solutions for a singular k-Hessian system
    Yang, Zedong
    Bai, Zhanbing
    DEMONSTRATIO MATHEMATICA, 2024, 57 (01)
  • [6] Boundary behavior of k-convex solutions for singular k-Hessian equations
    Sun, Huayuan
    Feng, Meiqiang
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2018, 176 : 141 - 156
  • [7] Classification and existence of positive entire k-convex radial solutions for generalized nonlinear k-Hessian system
    ZHANG Li-hong
    YANG Ze-dong
    WANG Guo-tao
    Mohammad M.Rashidi
    AppliedMathematics:AJournalofChineseUniversities, 2021, 36 (04) : 564 - 582
  • [8] Entire positive k-convex solutions to k-Hessian type equations and systems
    Bai, Shuangshuang
    Zhang, Xuemei
    Feng, Meiqiang
    ELECTRONIC RESEARCH ARCHIVE, 2022, 30 (02): : 481 - 491
  • [9] Classification and existence of positive entire k-convex radial solutions for generalized nonlinear k-Hessian system
    Zhang Li-hong
    Yang Ze-dong
    Wang Guo-tao
    Rashidi, Mohammad M.
    APPLIED MATHEMATICS-A JOURNAL OF CHINESE UNIVERSITIES SERIES B, 2021, 36 (04) : 564 - 582
  • [10] Classification and existence of positive entire k-convex radial solutions for generalized nonlinear k-Hessian system
    Li-hong Zhang
    Ze-dong Yang
    Guo-tao Wang
    Mohammad M. Rashidi
    Applied Mathematics-A Journal of Chinese Universities, 2021, 36 : 564 - 582
12345