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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Monotone iteration and Green’s functions for boundary value problems


Authors: P. W. Eloe and L. J. Grimm
Journal: Proc. Amer. Math. Soc. 78 (1980), 533-538
MSC: Primary 34B15; Secondary 34B27
DOI: https://doi.org/10.1090/S0002-9939-1980-0556627-7
MathSciNet review: 556627
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Abstract: An iteration scheme is given for approximating solutions of boundary problems of the form $Ly = f(x,y),Ty(x) = r$, where L is an nth order linear differential operator, f is continuous and T is a continuous linear operator from ${C^{n - 1}}(I)$ into ${{\mathbf {R}}^n}$. The scheme is based on the condition that the Green’s function $G(x,s)$ for the associated linear problem $Ly = 0,Ty = 0$ exists and has sign independent of s.


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Article copyright: © Copyright 1980 American Mathematical Society