Existence of Solutions to Elliptic Problem with Convection Term and Lower-Order Term. (28th October 2020) - He, Xiaohua; Huang, Shuibo; Tian, Qiaoyu; Xu, Yonglin
Abstract : In this paper, we establish the existence of solutions to the following noncoercivity Dirichlet problem − div M x ∇ u + u p − 1 u = − div u E x + f x, x ∈ Ω, u x = 0, x ∈ ∂ Ω, where Ω ⊂ ℝ N N > 2 is a bounded smooth domain with 0 ∈ Ω, f belongs to the Lebesgue space L m Ω 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.