Existence of Large Solutions for Quasilinear Elliptic Equation

Authors

  • Xiao Li Zhejiang Water Conservancy and Hydropower College, Zhejiang Hangzhou 310018
  • Zuodong Yang Institute of Mathematics, School of Mathematics Science, Nanjing Normal University, Jiangsu Nanjing 210046, China; and College of Zhongbei, Nanjing Normal University, Jiangsu Nanjing 210046

DOI:

https://doi.org/10.26713/cma.v2i2-3.134

Keywords:

Blow up, Large solution, Quasilinear elliptic equation, Upper-lower solution, Existence

Abstract

In this paper, we consider the problem \begin{align*}\begin{cases}-\mbox{\rm div}(|\nabla u|^{p-2}\nabla u)=\lambda u-b(x)h(u),&x\in \Omega\\u=+\infty, &\mbox{on}\ \partial\Omega.\end{cases}\end{align*}where $\Omega$ is a smooth bounded domain in ${\bf R^N}$. The weight function $b(x)$ is a non-negative continuous function in the domain, $h(u)$ is locally Lipschitz continuous, $h(u)/u^{p-1}$ is increasing on $(0,\infty)$ and $h(u)\sim Hu^{m(p-1)}$ for sufficiently large $u$ with $H>0$ and $m>1$. We establish conditions sufficient to ensure the existence of positive large solutions of the equation.

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Published

28-12-2011
CITATION

How to Cite

Li, X., & Yang, Z. (2011). Existence of Large Solutions for Quasilinear Elliptic Equation. Communications in Mathematics and Applications, 2(2-3), 87–95. https://doi.org/10.26713/cma.v2i2-3.134

Issue

Section

Research Article