Existence and Multiplicity of Radially Symmetric k-Admissible Solutions for Dirichlet Problem of k-Hessian Equations

Author:

He Zhiqian1,Miao Liangying2

Affiliation:

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

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

Abstract

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 { S k ( D 2 u ) = f ( u ) in B , u = 0 on B , and the corresponding one-parameter problem, where B is a unit ball in ℝ n 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.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

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