一类一阶半正周期边值问题正解的存在性

Existence of positive solutions for a class of first order semi-positone periodic boundary value problems

研究了一类一阶半正周期边值问题{u'(t)=λa(t)[f(u(t))-k],t∈[0,1],u(0)=u(1)正解的存在性,其中,k>0为常数,λ>0为参数。权函数a:[0,1]→R为连续函数,f或是定义在[0,∞)上的非负连续函数,满足f(0)=0且在无穷远处是次线性的,或是定义在(0,∞)上的正连续函数且在0处具有奇异性。运用上下解方法证明了该问题正解的存在性。

This paper studies the existence of positive solutions for a class of first order semi-positone periodic boundary value problemsìíîu'(t)=λa(t)[f(u(t))-k],t∈[0,1],u(0)=u(1),where k is a constant,k>0,λis a parameter,λ>0,a:[0,1]→R is a continuous function,either f is nonnegative and continuous on[0,∞)with f(0)=0 or f is positive and continuous in(0,∞)and singular at 0.The existence of positive solutions of the problems is obtained by applying the method of upper and lower solutions.