非线性二阶奇异边值问题正解存在的充分必要条件

A NECESSARY AND SUFFICIENT CONDITION FOR THE EXISTENCE OF POSITIVE SOLUTIONS TO NONLINEAR SECOND-ORDER SINGULAR BOUNDARY VALUE PROBLEMS

研究了奇异二阶边值问题u″ +a(t) f(u) +b(t) g(u) =0 ,αu(0 ) - βu′(0 ) =0 ,γu(1) +δu′(1)=0的正解 ,在a(t) ,b(t)只满足一定的可积性条件下得到了C1[0 ,1]正解存在的充分必要条件 ,从而推广了一些已知结果 ,使此类问题的适用范围更为广泛 .

A necessary and sufficient condition for the existence of C1 positive solutions of singular boundary value problem u″+a(t)f(u)+b(t)g(u)=0,αu(0)-βu′(0)=0,γu(1)+δu′(1)=0 is obtained, when a,b satisfy a certain kind of integrity conditions. This paper generalized some known results and enlarged the range of this kind of problem.