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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Singular perturbations and nonstandard analysis
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by S. Albeverio, J. E. Fenstad and R. Høegh-Krohn PDF
Trans. Amer. Math. Soc. 252 (1979), 275-295 Request permission

Abstract:

We study by methods of nonstandard analysis second order differential operators with zero order coefficients which are too singular to be defined by standard functions. In particular we study perturbations of the Laplacian in ${R^3}$ given by potentials of the form $\lambda {\Sigma _j}\delta \left ( {x - {x_j}} \right )$. We also study Sturm-Liouville problems with zero order coefficients given by measures and prove that they satisfy the same oscillation theorems as the regular Sturm-Liouville problems.
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Additional Information
  • © Copyright 1979 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 252 (1979), 275-295
  • MSC: Primary 34B25; Secondary 03H05, 26E35, 35P99
  • DOI: https://doi.org/10.1090/S0002-9947-1979-0534122-5
  • MathSciNet review: 534122