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C. V. Pao 《Progress in Nuclear Energy》1981,8(2-3):191-202
When the effect of temperature feedback in a reactor system is considered the neutron transport equation for the neutron density is supplemented by a temperature equation which is a partial differential equation of parabolic type if heat conduction is taken into consideration. This consideration leads to a coupled system of nonlinear partial integro-differential equations. The aim of this paper is to present an iterative scheme for the determination of the solution of the nonlinear coupled system and to establish some qualitative property of the solution. The iterative scheme consists of two monotone sequences which converge monotonically from above and below, respectively, to a unique solution. The qualitative aspect includes the existence and uniqueness of a positive solution, upper and lower bounds of the solution and stability of a steady-state solution. 相似文献
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讨论了n阶非线性微分方程y^(n)=f(t,y‘,…,…,y^(n-1)满足边界条件y^(n-3)(α)+λαy^(n-2)(α)=λ1,y^(n-1)(β)=λn-1,y^(n-3)(4)+λny^(n-2)(r)=λn+1,或y^(n-2(α)+λαy^(n-1)(α)=λ1,y^j)(β)=γj+2(j=0,1,…,n-3),y^(n-2)(4)+λny^(n-1)(4)=λn+1的三点问题 相似文献
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王殿选 《东北电力学院学报》1998,18(2):39-43
讨论了n阶非线性微分方程y(n)=f(t,y,y′,…,y(n-1)满足边界条件y(n-3)(α)+λ0y(n-2)(α)=λ1,y(n-1)(β)=λn-1,y(γ)=λn,n≥3,y(j)(β)=λj+2(j=0,1,…,n-4),n>3或y(n-2)(α)+λ0y(n-1)(α)=λ1,y(j)(β)=λj+2(j=0,1,…,n-3),y(γ)=λn的边值问题解的存在唯一性,其中α,β,γ及λi(i=0,1,…,n)均为实数。通篇假设函数f(t,y1,y2,…,yn)是区域[α,γ]×Rn上的连续函数。 相似文献
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