Journal of the Korean Society of Industry Convergence (한국산업융합학회 논문집)

The Korean Society of Industry Convergence (한국산업융합학회)
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Application of Implicit Function Theorem to Existence of Solutions to Ordinary Differential Equations with Nonlocal Boundary Conditions, II

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

  • Do, Tae-Sug (Dept. of Mathematics Education, College of Education, Kwandong University)
  • 도태석 (관동대학교 사범대학 수학교육학과)
  • Received : 2002.07.03
  • Accepted : 2002.10.10
  • Published : 2002.11.30
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Abstract

We consider the problem y"=a(x,y)(y-b), (0$$y(0)=0,\;y^{\prime}(1)=g(y({\xi}),\;y^{\prime}({\xi})),\;{\xi}$$ 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.

Keywords