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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

1. Allegretto, W., Oscillation criteria for quasilinear equations, Canad. J. Math. 26 (1974), 931-947.Google Scholar
2. Atkinson, F. V., On second-order differential inequalities, Proc. Roy. Soc. Edinburgh, Sect. A, 72 (1974), 109-127.Google Scholar
3. Kartsatos, A. G., On the maintenance of oscillations of nth order equations under the effect of a small forcing term, J. Differential Equations 10 (1971), 355-363.Google Scholar
4. Kartsatos, A. G.,Maintenance of oscillations under the effect of a periodic forcing term, Proc. Amer. Math. Soc. 33 (1972), 377-383.Google Scholar
5. Kitamura, Y. and Kusano, T., An oscillation theorem for a sublinear Schrödinger equation, Utilitas Math. 14 (1978), 171-175.Google Scholar
6. Kreith, K., Oscillation Theory, Lecture Notes in Mathematics, Vol. 324, Springer Verlag, Berlin, 1973.Google Scholar
7. Noussair, E. S. and Swanson, C. A.,Oscillation theory for semilinear Schrödinger equations and inequalities, Proc. Roy. Soc. Edinburgh, Sect. A, 75 (1975/76), 67-81.Google Scholar
8. Noussair, E. S. and Swanson, C. A., Oscillation of semilinear elliptic inequalities by Riccati transformations, Canad. J. Math., to appear.Google Scholar
9. Swanson, C. A., Semilinear second order elliptic oscillation, Canad. Math. Bull. 22 (1979), 139-157.Google Scholar