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Oscillation Criteria for a Class of Perturbed Schrödinger Equations
Published online by Cambridge University Press: 20 November 2018
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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.
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- 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
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