Minkowski空间一维给定平均曲率型方程Robin问题正解的存在性和多解性

基于锥上的不动点指数理论, 通过构造适当的锥, 讨论Minkowski空间中一维给定平均曲率方程Robin问题正解的存在性和多解性, 得到了非线性项f的零点个数与该Robin问题正解个数的关系. 其中: λ是正参数; a∈C［0,1］; f∈C(［0,∞),［0,∞))满足存在两个正的点列a_i,b_i(i=1,2,…,n), a_ii≤a_i+1i+1, 使得f(a_i)=0, f(b_i)=0且f(s)>0, s∈(a_i,b_i).

Existence and Multiplicity of Positive Solutions for Robin Problem of One-Dimensional Prescribed Mean Curvature Equation in Minkowski Space

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.