【摘要】 考察如下边值问题正解的存在性x″(t) +λa(t) f (x(t) ,y(t) ) =0y″(t) +λb(t) g(x(t) ,y(t) ) =0x(0 ) =x(1 ) =y(0 ) =y(1 ) =0其中 f ,g:R+× R+ R+;a,b:[0 ,1 ] R+.所有的函数都被假定是连续的 ,此外 f ,g满足某些增长性条件 .本文得到了一些正解的存在性结果 .更多还原

【Abstract】 The existence of positive solutions of boundary value problemx″(t)+λa(t)f(x(t),y(t))=0 y″(t)+λb(t)g(x(t),y(t))=0 x(0)=x(1)=y(0)=y(1)=0is investigated where f and g are functions from R +×R + into R +; and a,b are functions from [0,1] into R +. All functions are assumed to be continuous, and some growth conditions are imposed on f and g. We get some results about the existence of positive solution.更多还原