Existence and multiplicity of radially symmetric k-admissible solutions for Dirichlet problem of k-Hessian equations

Authors

  • Zhiqian He Qinghai University
  • Liangying Miao Qinghai Nationalities University

DOI:

https://doi.org/10.1515/ms-2022-0008

Keywords:

k-Hessian equation, admissible solution, multiplicity, Leggett-Williams' fixed point theorem

Abstract

In this paper, we study the existence and multiplicity of radially symmetric k-admissible solutions for the k-Hessian equation with 0-Dirichlet boundary condition

Sk(D2 u)= f(-u) in B
u=0                        on ∂B

and the corresponding one-parameter problem, where B is a unit ball in Rn with n ≥ 1, k∈ {1, ... , n}, f: [0, +∞) → [0, +∞) is continuous. We show that the k-admissible solutions are not convex, so we construct a new cone and obtain the existence of triple and arbitrarily many k-admissible solutions via the Leggett-Williams' fixed point theorem.

 

Author Biographies

Zhiqian He, Qinghai University

Department of Basic Teaching and Research
Qinghai University
Xining 810016
P.R.CHINA

Liangying Miao, Qinghai Nationalities University

School of Mathematics and Statistics
Qinghai Nationalities University
Xining
810007
P.R.CHINA

Published

2022-02-16

Issue

Section

Articles - Other topics