In this paper,we will study the nonlocal and nonvariational elliptic problem{−(1+a||u||_(q)^(αq))Δu=|u|^(p−1)u+h(x,u,∇_(u))inΩ,u=0 on∂Ω,(0.1)(1)where a>0,α>0,1<q<2^(∗),p∈(0,2^(∗)−1)∖{1}andΩis a boun...In this paper,we will study the nonlocal and nonvariational elliptic problem{−(1+a||u||_(q)^(αq))Δu=|u|^(p−1)u+h(x,u,∇_(u))inΩ,u=0 on∂Ω,(0.1)(1)where a>0,α>0,1<q<2^(∗),p∈(0,2^(∗)−1)∖{1}andΩis a bounded smooth domain in R^(N)(N≥2).Under suitable assumptions about h(x,u,∇u),we obtain\emph{a priori}estimates of positive solutions for the problem(0.1).Furthermore,we establish the existence of positive solutions by making use of these estimates and of the method of continuity.展开更多
基金supported by National Natural Science Foundation of China(11801167)Hunan Provincial Natural Science Foundation of China(2019JJ50387).
文摘In this paper,we will study the nonlocal and nonvariational elliptic problem{−(1+a||u||_(q)^(αq))Δu=|u|^(p−1)u+h(x,u,∇_(u))inΩ,u=0 on∂Ω,(0.1)(1)where a>0,α>0,1<q<2^(∗),p∈(0,2^(∗)−1)∖{1}andΩis a bounded smooth domain in R^(N)(N≥2).Under suitable assumptions about h(x,u,∇u),we obtain\emph{a priori}estimates of positive solutions for the problem(0.1).Furthermore,we establish the existence of positive solutions by making use of these estimates and of the method of continuity.
