the generalized green’s function for boundary value problem of second order difference equation

la función de Green generalizada para el problema de valores en la frontera de una ecuación en diferencias de segundo orden

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2015
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Abstract
Let b>a+2 and [a+1,b+1]={a+1,a+2,…,b+1}. In this paper, by building the generalized Green’s function for the problems, we study the solvability of the S-L problem Lx=Δ[p(t-1)Δx(t-1)]+[q(t)+λr(t)]x(t)=-f(t), U1(x)=α1x(a)+α2Δx(a)=0, U2(x)=β1x(b+1)+β2Δx(b+1)=0, and the periodic S-L problem Lx=Δ[p(t-1)Δx(t-1)]+[q(t)+λr(t)]x(t)=-f(t), U3(x)=x(a)-x(b+1)=0, U4(x)=Δx(a)-Δx(b+1)=0, where the parameter λ is an eigenvalue of the linear problem Lx=0, U1(x)=0, U2(x)=0 or the problem Lx=0, U3(x)=0, U4(x)=0, and p:[a,b+1]→(0,+∞),r:[a+1,b+1]→(0,+∞), q(t) is defined and real valued on [a+1,b+1], α12+α22≠0,β12+β22≠0, and in the periodic S-L problem we have p(a)=p(b+1).
Sean b>a+2 y [a+1,b+1]={a+1,a+2,…,b+1}. En este trabajo, mediante la construcción de la función de Green generalizada para los problemas, estudiamos la resolubilidad del problema de S-L Lx=Δ[p(t-1)Δx(t-1)]+[q(t)+λr(t)]x(t)=-f(t), U1(x)=α1x(a)+α2Δx(a)=0, U2(x)=β1x(b+1)+β2Δx(b+1)=0, y del problema periódico de S-L Lx=Δ[p(t-1)Δx(t-1)]+[q(t)+λr(t)]x(t)=-f(t), U3(x)=x(a)-x(b+1)=0, U4(x)=Δx(a)-Δx(b+1)=0, donde el parámetro λ es un autovalor del problema lineal Lx=0, U1(x)=0, U2(x)=0 o del problema Lx=0, U3(x)=0, U4(x)=0, y p:[a,b+1]→(0,+∞),r:[a+1,b+1]→(0,+∞), q(t) está definida y toma valores reales en [a+1,b+1], α12+α22≠0,β12+β22≠0, y en el problema periódico de S-L se tiene p(a)=p(b+1).
Reference Key
han2015journalthe Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Xiaoling Han, Juanjuan Huang
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Journal Biosensors
Year 2015
DOI
10.1155/2015/201946
URL
http://dx.doi.org/10.1155/2015/201946
Keywords
ophthalmology fermentation mathematics myanmar ethnic food

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