CAJ | 학술논문

应用Green函数可以将微分方程边值问题转化为等价的积分方程.近来此方法被应用于讨论微分方程边值问题正解的存在性.本文讨论非线性二阶Neumann边值问题,应用Green函数,将其转化为等价的积分方程,并设非线性项在无穷远处有增长条件,利用锥上的不动点指数理论证明正解的存在性和非存在性.
응용Green함수가이장미분방정변치문제전화위등개적적분방정.근래차방법피응용우토론미분방정변치문제정해적존재성.본문토론비선성이계Neumann변치문제,응용Green함수,장기전화위등개적적분방정,병설비선성항재무궁원처유증장조건,이용추상적불동점지수이론증명정해적존재성화비존재성.
By the means of the Green's function,the boundary value problem of differential equation can be reduced to the equivalent integral equation.Recently,this method is used successfully to discuss the existence of the positive solutions to the boundary value problem of nonlinear differential equation.This article investigates the nonlinear Neumann boundary value problem.Applying growth conditions on the nonlinear terms,we obtain the existence and nonxistence results for the positive solutions by the fixed point index theory in cones.