数学物理学报(英文版)

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NECESSARY AND SUFFICIENT CONDITIONS FOR THE EXISTENCE OF NONNEGATIVE SOLUTIONS OF INHOMOGENEOUS p-LAPLACE EQUATION

戴求亿; 彭丽辉   

  1. 湖南师范大学数学与计算机学院, 长沙 410081
  • 收稿日期:2004-10-09 修回日期:2005-09-25 出版日期:2007-01-20 发布日期:2007-01-20
  • 通讯作者: 戴求亿
  • 基金资助:

    This work is supported by NNSF of China (10171029)

NECESSARY AND SUFFICIENT CONDITIONS FOR THE EXISTENCE OF NONNEGATIVE SOLUTIONS OF INHOMOGENEOUS p-LAPLACE EQUATION

Dai Qiuyi; Peng Lihui   

  1. Department of Mathematics, Hunan Normal University, Changsha 410081, China
  • Received:2004-10-09 Revised:2005-09-25 Online:2007-01-20 Published:2007-01-20
  • Contact: Dai Qiuyi

摘要:

Let $\Omega$ be a smooth bounded domain in Rn. In this article, we consider the homogeneous boundary Dirichlet problem of inhomogeneous $p$-Laplace equation $-\Delta_p u=|u|^{q-1}u+\lambda f(x)$ on $\Omega$, and identify necessary and sufficient conditions on $\Omega$ and $f(x)$ which ensure the existence, or multiplicities of nonnegative solutions for the problem under consideration.

关键词: Inhomogeneous p-Laplace equation, Dirichlet problem, nonnegative solution

Abstract:

Let $\Omega$ be a smooth bounded domain in Rn. In this article, we consider the homogeneous boundary Dirichlet problem of inhomogeneous $p$-Laplace equation $-\Delta_p u=|u|^{q-1}u+\lambda f(x)$ on $\Omega$, and identify necessary and sufficient conditions on $\Omega$ and $f(x)$ which ensure the existence, or multiplicities of nonnegative solutions for the problem under consideration.

Key words: Inhomogeneous p-Laplace equation, Dirichlet problem, nonnegative solution

中图分类号: 

  • 35J15