数学物理学报 ›› 2019, Vol. 39 ›› Issue (3): 535-544.

• 论文 • 上一篇    下一篇

一类非线性双调和方程在${{\mathbb{R}}^{N}}$上正整解存在的充分必要条件

欧笑杭()   

  1. 顺德职业技术学院 广东佛山 528333
  • 收稿日期:2018-02-13 出版日期:2019-06-26 发布日期:2019-06-27
  • 作者简介:欧笑杭, sdouxh@126.com

Sufficient and Necessary Condition for the Existence of Positive Entire Solutions of a Nonlinear Biharmonic Equations on ${{\mathbb{R}}^{N}}$

Xiaohang Ou()   

  1. Shunde Polytechnic, Guangdong Foshan 528333
  • Received:2018-02-13 Online:2019-06-26 Published:2019-06-27

摘要:

研究一类形如$\triangle^2u=f(|x|, u, |\nabla u|)(x\in \mathbb{R} ^N, N>2)$的非线性双调和方程,证明了其在$\mathbb{R} ^N$上存在正整解的充分必要条件,并给出了解的一些性质.

关键词: 非线性双调和方程, 正整解, 闭凸子集, 等度连续, 不动点定理

Abstract:

The aim of this paper is to study the nonlinear biharmonic equations of the following form $\triangle^2u=f(|x|, u, |\nabla u|)(x\in \mathbb{R} ^N, N>2)$. The Sufficient and necessary condition for the existence of positive entire solutions is proved, and some properties of the solutions are obtained.

Key words: Nonlinear biharmonic equation, Positive entire solution, Close convex subset, Equicontinuity, Fixed point theorem

中图分类号: 

  • O175.25