The authors study the existence of solutions for the nonlinear elliptic system {-Mλ+,(D2u)=f(u,v)in Ω,-Mλ+,(D2u)=g(u,v)inΩ,u≥0,v≥0 inΩ,u=v=0 on Ω, where Ω is a bounded convex domain in RN, N ≥ 2. I...The authors study the existence of solutions for the nonlinear elliptic system {-Mλ+,(D2u)=f(u,v)in Ω,-Mλ+,(D2u)=g(u,v)inΩ,u≥0,v≥0 inΩ,u=v=0 on Ω, where Ω is a bounded convex domain in RN, N ≥ 2. It is shown that under some assumptions on f and g, the problem has at least one positive solution (u, v).展开更多
The solution of a nonlinear elliptic equation involving Pucci maximal operator and super linear nonlinearity is studied. Uniqueness results of positive radial solutions in the annulus with Dirichlet boundary condition...The solution of a nonlinear elliptic equation involving Pucci maximal operator and super linear nonlinearity is studied. Uniqueness results of positive radial solutions in the annulus with Dirichlet boundary condition are obtained. The main tool is Lane-Emden transformation and Koffman type analysis. This is a generalization of the corresponding classical results involving Laplace operator.展开更多
基金supported by National Natural Sciences Foundations of China (10571175,10631030)
文摘The authors study the existence of solutions for the nonlinear elliptic system {-Mλ+,(D2u)=f(u,v)in Ω,-Mλ+,(D2u)=g(u,v)inΩ,u≥0,v≥0 inΩ,u=v=0 on Ω, where Ω is a bounded convex domain in RN, N ≥ 2. It is shown that under some assumptions on f and g, the problem has at least one positive solution (u, v).
基金National Natural Science Foundation of China(11101141)Scientific Research Foundation for the Returned Overseas Chinese Scholars of the State Education MinistryDoctoral Funding of North China Electric Power University
文摘The solution of a nonlinear elliptic equation involving Pucci maximal operator and super linear nonlinearity is studied. Uniqueness results of positive radial solutions in the annulus with Dirichlet boundary condition are obtained. The main tool is Lane-Emden transformation and Koffman type analysis. This is a generalization of the corresponding classical results involving Laplace operator.