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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Estimates for Green’s functions
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by A. G. Ramm and Lige Li
Proc. Amer. Math. Soc. 103 (1988), 875-881
DOI: https://doi.org/10.1090/S0002-9939-1988-0947673-7

Abstract:

Let ${l_q} = - {\nabla ^2} + q(x),x \in {R^3},0 \leq q \leq c{(1 + \left | x \right |)^{ - a}},a{\text { > }}2,{l_q}{G_q}(x,y) = \delta (x - y)$. If $q \geq p \geq 0,q \not \equiv p$, then $\begin {gathered} c\left | {x - y\left | {^{ - 1}} \right .{\text { < }}{{\text {G}}_q}(x,y){\text { < }}} \right .{G_p}(x,y) \leq {(4\pi \left | {x - y} \right |)^{ - 1}},x \ne y \end {gathered}$, for some positive $c = c(q)$. If $p \not \equiv 0$ then ${G_p}{\text { < }}{(4\pi \left | {x - y} \right |)^{ - 1}},x \ne y$.
References
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Bibliographic Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 103 (1988), 875-881
  • MSC: Primary 35J15; Secondary 35A08
  • DOI: https://doi.org/10.1090/S0002-9939-1988-0947673-7
  • MathSciNet review: 947673