Existence and NonExistence of Solutions to Some Degenerate Coercivity Quasilinear Elliptic Equations with Measure Data 
Received:March 03, 2021 Revised:April 28, 2021 
Key Words:
elliptic equation degenerate coercivity measures data existence nonexistence

Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11761059), Program for Yong Talent of State Ethnic Affairs Commission of China (Grant No.XBMU2019AB34), Fundamental Research Funds for the Central Universities (Grant No.31920200036), Innovation Team Project of Northwest Minzu University (Grant No.1110130131) and Firstrate Discipline of Northwest Minzu University (Grant No.2019XJYLZY02). 
Author Name  Affiliation  Maoji RI  School of Mathematics and Computer Science, Northwest Minzu University, Gansu 730030, P. R. China  Xiangrui LI  School of Mathematics and Computer Science, Northwest Minzu University, Gansu 730030, P. R. China  Qiaoyu TIAN  School of Mathematics and Computer Science, Northwest Minzu University, Gansu 730030, P. R. China  Shuibo HUANG  School of Mathematics and Computer Science, Northwest Minzu University, Gansu 730030, P. R. China Key Laboratory of Streaming Data Computing Technologies and Application, Northwest Minzu University, Gansu 730030, P. R. China 

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Abstract: 
In this article, we study the existence and nonexistence of weak solutions to the following quasilinear elliptic problem with principal part having degenerate coercivity and nonlinear term involving gradient, $$\left \{\begin{array}{ll}\text{div}(\frac{\nabla u^{p2}\nabla u}{(1+u)^{\theta(p1)}})+\frac{u^{p2}u\nabla u^{p}}{(1+u)^{\theta p}}=\mu,~&x\in\Omega,\\ u=0,~&x\in\partial\Omega,\end{array}\right.$$ where $\Omega\subseteq\mathbb{R}^N~(N\geq3)$ is a bounded smooth domain, $1 
Citation: 
DOI:10.3770/j.issn:20952651.2022.02.008 
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