关键词: 平均曲率问题, 不动点指数, 正解, 正解的个数

Abstract: Based on the fixed point index theorem of cone, by constructing a proper cone, we discuss the existence and multiplicity of positive solutions for Robin problem of one-dimensional prescribed mean curvature equation in Minkowski space and obtain relationship between the number of the zeros of the nonlinear term f and the number of positive solutions of the Robin problems, where λ is a positive parameter, a∈C［0,1］, f∈C(［0,∞),［0,∞)) and there exist two sequences of positive numbers a_i and b_i with f(a_i)=0, f(b_i)=0 and f(s)>0 in s∈(a_i,b_i), and a_ii≤a_i+1i+1 for i=1,2,…,n.

Key words: mean curvature problem, fixed point index, positive solution, number of positive solution