Minkowski空间中含平均曲率算子的拟线性微分系统Dirichlet问题径向正解的唯一性

Uniqueness of Positive Radial Solutions of Dirichlet Problemfor Quasilinear Differential System with Mean Curvature Operator in Minkowski Space

基于锥上不动点指数理论,讨论含平均曲率算子的拟线性微分系统Dirichlet问题{M(u)+f_(1)(v)=0,x∈B,M(v)+f_(2)(u)=0,x∈B,u|∂B=v|∂B=0径向正解的唯一性,其中M(w)∶=div(■w/√1-|■w|^(2)),f_(i)∈C([0,∞),[0,∞)),i=1,2,B为ℝ^(N)(N≥2)空间中的单位球.

Based on the fixed point index theorem,we discuss the uniqueness of positive radial solutions of Dirichlet problem for quasilinear differential system with mean curvature operator M(u)+f_(1)(v)=0,x∈B,M(v)+f_(2)(u)=0,x∈B,u|∂B=v|∂B=0,where M(w)∶=div(■w/√1-|■w|^(2)),f i∈C([0,∞),[0,∞)),i=1,2,B is the unit ball in ℝ^(N)(N≥2).