Existence and Non-Existence of Solutions to Some Degenerate Coercivity Quasilinear Elliptic Equations with Measure Data
Received:March 03, 2021  Revised:April 28, 2021
Key Word: elliptic equation   degenerate coercivity   measures data   existence   non-existence  
Fund ProjectL: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.XBMU-2019-AB-34), Fundamental Research Funds for the Central Universities (Grant No.31920200036), Innovation Team Project of Northwest Minzu University (Grant No.1110130131) and First-rate Discipline of Northwest Minzu University (Grant No.2019XJYLZY-02).
Author NameAffiliation
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 non-existence of weak solutions to the following quasilinear elliptic problem with principal part having degenerate coercivity and nonlinear term involving gradient, $$\left \{\begin{array}{ll}-\text{div}(\frac{|\nabla u|^{p-2}\nabla u}{(1+|u|)^{\theta(p-1)}})+\frac{|u|^{p-2}u|\nabla u|^{p}}{(1+|u|)^{\theta p}}=\mu,~&x\in\Omega,\\ u=0,~&x\in\partial\Omega,\end{array}\right.$$ where $\Omega\subseteq\mathbb{R}^N~(N\geq3)$ is a bounded smooth domain, $1
Citation:
DOI:10.3770/j.issn:2095-2651.2022.02.008
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