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

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

We consider the problem y"=a(x,y)(y-b), (0<x<1) $$y(0)=0,\;y^{\prime}(1)=g(y({\xi}),\;y^{\prime}({\xi})),\;{\xi}$$ fixed in (0,1). This is a model of steady-state 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, and positivity of solutions.

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