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 gradie,{-div(|∇u|p...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 gradie,{-div(|∇u|p−2∇u/(1+|u|)θ(p−1))+|u|p−2u|∇u|p/(1+|u|)θp=μ,x∈Ω,u=0,x∈■ΩwhereΩ■R^(N)(N≥3)is a bounded smooth domain,1,μis a Radon measure.展开更多
基金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)+2 种基金Fundamental Research Funds for the Central Universities(Grant No.31920200036)Innovation Team Project of Northwest Minzu University(Grant No.1110130131)First-rate Discipline of Northwest Minzu University(Grant No.2019XJYLZY-02)。
文摘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 gradie,{-div(|∇u|p−2∇u/(1+|u|)θ(p−1))+|u|p−2u|∇u|p/(1+|u|)θp=μ,x∈Ω,u=0,x∈■ΩwhereΩ■R^(N)(N≥3)is a bounded smooth domain,1,μis a Radon measure.
