关键词: 周期边值问题, 半正, 不定权, 正解, Krasnoselskill不动点定理

Abstract: The author considers the existence of positive solutions for the first-order semi-positone problem. Based on the fixed point theorem of  Krasnoselskill, the author proves that there exists λ*>0, such that the problem has at least one solution when 0<λ<λ*.

Key words: periodic boundary value problem, semi-positone, discretion, positive solution, fixed point theorem of Krasnoselskill