关键词: 正解, 多解性, 上下解方法, 拓扑度

Abstract: By using the method of upper and lower solution and topological degree theory, the author considered the existence and multiplicity of positive solutions of a class of first-order nonlinear boundary value problems. The results show that  there is  a positive number b*, so that there are  at least two positive solutions to the problem when  0<b<b*, there is exactly one positive solution to the problem when b=b*, there is no positive solution to the problem when b>b*, where b is a positive parameter, a∈C(［0,1］,［0,∞)) and is not always 0 on any subinterval of ［0,1］, f∈C(［0,+∞),［0,+∞)).

Key words:  , positive solution, multiplicity, method of upper and lower solution, topological degree