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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Monotone iteration and Green’s functions for boundary value problems
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by P. W. Eloe and L. J. Grimm PDF
Proc. Amer. Math. Soc. 78 (1980), 533-538 Request permission

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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Additional Information
  • © Copyright 1980 American Mathematical Society
  • 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