Existence And Non-existence Of Solutions To Some Degenerate Coercivity Elliptic Equations Involving Measures Data

In this paper,we consider the existence and non-existence of solutions to three kinds of elliptic problem with principal part having degenerate coercivity by weak convergence methods.The article is divided into three parts.Firstly,we study the non-existence of entropy solutions to the following quasilinear elliptic problem#12 Provided#12 where Ω is a bounded smooth subset ofRN(N>2),1<p<N,q>1,0 ≤θ<1,λ is a Radon measure.Secondly,we study the existence and non-existence of weak solutions to the following quasilinear elliptic problem with nonlinear term involving gradient#12 where μ is a Radon measure.Finally,we investigate the existence of(?)(Ω)solutions to the following nonlinear elliptic equation with singular quadratic lower order term#12 where γ>0,N/N-1≤θ<2,f∈Lm(Ω)(m≥1)is a non-negative function.