Existence of Solutions to Elliptic Problem with Convection Term and Lower-Order Term

In this paper, we establish the existence of solutions to the following noncoercivity Dirichlet problem −divMx∇u+up−1u=−divuEx+fx,x∈Ω,ux=0,x∈∂Ω, where Ω⊂ℝNN>2 is a bounded smooth domain with 0∈Ω, f belongs to the Lebesgue space LmΩ with m≥1,p>0. The main innovation point of this paper is the combined effects of the convection terms and lower-order terms in elliptic equations