Singular perturbations and nonstandard analysis

Authors:
S. Albeverio, J. E. Fenstad and R. Høegh-Krohn

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

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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 given by potentials of the form . 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

DOI:
https://doi.org/10.1090/S0002-9947-1979-0534122-5

Keywords:
Singular perturbations,
Schrödinger operators,
Sturm-Liouville problems,
nonstandard analysis

Article copyright:
© Copyright 1979
American Mathematical Society