Boundary behavior of large solutions to -Laplacian elliptic equations

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• 作者：Zhijun Zhang ^{chinazjzhang2002@163.com" class="auth_mail" title="E-mail the corresponding author zhangzj@ytu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：pp-Laplacian elliptic equations ; Large solutions ; Boundary behavior
• 刊名：Nonlinear Analysis: Real World Applications
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：33
• 期：Complete
• 页码：40-57
• 全文大小：686 K

文摘

This paper is concerned with exact asymptotic behavior near the boundary of large solutions to quasilinear elliptic equations ${△}_{p}u\left(x\right)=b\left(x\right)f\left(u\left(x\right)\right),x\in \Omega$, where Ω$\Omega$ is a bounded smooth domain in R^N${\mathbb{R}}^N$, ${△}_{p}u=\mathrm{div}\left({\left|\nabla u\right|}^{p-2}\nabla u\right)$ with p>1$p>1$, and b∈C(Ω)$b\in C\left(\Omega \right)$ is nonnegative in Ω$\Omega$, but may be vanishing or appropriately singular (including critical singular) on the boundary. We give one new condition near infinity on f$f$ which plays a crucial role in the boundary behavior of solutions.