带有指数型非线性项的一维Minkowski-曲率方程

One-dimensional Minkowski-curvature Equation with Exponential Nonlinearity

研究一维Minkowski空间中给定平均曲率方程Dirichlet问题:-(u′[]1-u′2)′=λe u,x∈(-L,L),u(-L)=0=u(L)正解的确切个数及分歧图,其中λ>0,0<L≤1为参数.运用时间映像原理,获得了λ>0时该问题恰有一个正解.

In this paper,the exact multiplicity of positive solutions of the one-dimensional Minkowski-curvature equation with Dirichlet boundary conditions was studied-(u′[]1-u′2)′=λe u,x∈(-L,L),u(-L)=0=u(L),whereλ>0,0<L≤1 were parameters.By using a detailed analysis of time maps,it was obtained that the above problem had exactly one positive for anyλ>0.