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Oscillation Criteria for a Class of Perturbed Schrödinger Equations

Published online by Cambridge University Press:  20 November 2018

Takaŝi Kusano  and
Manabu Naito
Takaŝi Kusano
Affiliation:
Hiroshima University, Hiroshima 730, Japan
Manabu Naito
Affiliation:
Hiroshima University, Hiroshima 730, Japan
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We are concerned with the oscillatory behavior of the second order elliptic equation

1

where Δ is the Laplace operator in n-dimensional Euclidean space Rn, E is an exterior domain in Rn, and c:E × R → R and f:E → R are continuous functions.

A function v : E − R is called oscillatory in E if v(x) has arbitrarily large zeros, that is, the set {x ∈ E : v(x) = 0} is unbounded. For brevity, we say that equation (1) is oscillatory in E if every solution u ∈ C2(E) of (1) is oscillatory in E.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 25 , Issue 1 , 01 March 1982 , pp. 71 - 77
Copyright
Copyright © Canadian Mathematical Society 1982

References

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