Electronic Journal of Differential Equations,
Vol. 2019 (2019), No. 97, pp. 1-22.

Title: Entropy solutions to noncoercive nonlinear elliptic equations with measure data

Authors: Shuibo Huang (Northwest Minzu Univ., Lanzhou, Gansu, China)
         Tong Su      (Northwest Minzu Univ., Lanzhou, Gansu, China)
         Xinsheng Du  (Qufu Normal Univ., Qufu, Shandong, China)
         Xinqiu Zhang (Qingdao Univ., Qingdao, China)
 
Abstract:
 Let $\Omega\subseteq \mathbb{R}^N$ be a bounded domain.
 In this article, we investigate the existence of entropy solutions to
 the nonlinear elliptic problem
 $$\displaylines{
 -\hbox{div}\Big(\frac{|\nabla u|^{(p-2)}
 \nabla u+c(x)u^\gamma}{(1+|u|)^{\theta(p-1)}}\big)
  +\frac{b(x)|\nabla u|^\lambda}{(1+|u|)^{\theta(p-1)}}=\mu,\quad x\in\Omega, \cr
 u(x)=0,\quad x\in \partial\Omega,
 }$$
 where $\mu$  is a  diffuse measure with bounded variation on $\Omega$,
 $0\leq\theta<1$ is a positive constants,  1&lt;p&lt;N, $0&lt;\gamma\leq p-1$,
 $0&lt;\lambda\leq p-1$,  c(x) and b(x) belong to appropriate Lorentz spaces.

Submitted August 4, 2017. Published August 05, 2019.
Math Subject Classifications: 35R06, 35J70.
Key Words: Entropy solution; noncoercive;  nonlinear elliptic equations;
           measure data