Stability for noncoercive elliptic equations
Shuibo Huang, Qiaoyu Tian, Jie Wang, Jia Mu · DOAJ (DOAJ: Directory of Open Access Journals) · 2016
In this article, we consider the stability for elliptic problems that have degenerate coercivity in their principal part, $$\displaylines{ -\text{div}\Big(\frac{| abla u|^{p-2} abla u}{(1+|u|)^{\theta(p-1)}}\Big) +|u|^{q-1}u=f,\quad x\in\Omega, \cr u(x)=0,\quad x\in \partial\Omega, }$$ where $\theta>0$, $\Omega\subseteq \mathbb{R}^N$ is a bounded domain. Let K be a compact subset in $\Omega$ with zero r-capacity ($p r(p-1)[1+\theta(p-1)]/(r-p)$, and $u_n$ is the sequence of solutions of the corresponding problems with datum $f_n$. Then $u_n$ converges to the solution u.