Application of Implicit Function Theorem to Existence of Solutions to Ordinary Differential Equations with Nonlocal Boundary Conditions, I

비국소 경계 조건들을 가진 상미분 방정식들의 근의 존재성에 음함수 정리들의 응용 I

We consider the problem y"=a(x,y)(y-b), y(0)=0, y'(1)=g(y(${\xi}$), y'(${\xi}$)), (0${\xi}$ fixed in(0,1)) as a model of steady-slate heat conduction in a rod when the heat flux at the end x = 1 is determined by observation of the temperature and heat flux at some interior point ${\xi}$. We establish conditions sufficient for existence, uniqueness.