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An oscillation theorem for sublinear elliptic differential inequalities

Published online by Cambridge University Press:  17 April 2009

Norio Yoshida
Affiliation:
Department of Mathematics, Faculty of Engineering, Iwate University, Morioka, Japan.
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Abstract

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Sublinear elliptic differential inequalities with variable coefficients are studied. Sufficient conditions are given that all solutions are oscillatory in exterior domains. Riccati inequalities are used to establish sublinear oscillation criteria.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Itô, Seizô, “Fundamental solutions of parabolic differential equations and boundary value problems”, Japan. J. Math. 27 (1957), 55102.Google Scholar
[2]Kitamura, Yuichi and Kusano, Takaŝi, “An oscillation theorem for a sublinear Schrödinger equation”, Utilitas Math. 14 (1978), 171175.Google Scholar
[3]Kura, Takeshi, “Oscillation criteria for a class of sublinear elliptic equations of the second order”, Utilitas Math. 22 (1982), 335341.Google Scholar
[4]Levine, Howard A. and Payne, Lawrence E., “On the nonexistence of entire solutions to nonlinear second order elliptic equations”, SIAM J. Math. Anal. 7 (1976), 337343.Google Scholar
[5]Noussair, Ezzat S. and Swanson, Charles A., “Oscillation of semilinear elliptic inequalities by Riccati transformations”, Canad. J. Math. 32 (1980), 908923.CrossRefGoogle Scholar
[6]Onose, Hiroshi, “Oscillation criteria for sublinear Schrödinger equation”. Proc. Amer. Math. Soc. 85 (1982), 6972.Google Scholar
[7]Suleimanov, N.M., “On the behaviour of solutions of second order nonlinear elliptic equations with linear principal part”, Dokl. Akad. Nauk SSSR, 247 (1979), 805809.Google Scholar
[8]Swanson, Charles A., “Semilinear second order elliptic oscillation”, Canad. Math. Bull. 22 (1979), 139157.CrossRefGoogle Scholar
[9]Yoshida, Norio, “Oscillation properties of solutions of second order elliptic equations”, SIAM J. Math. Anal. 14 (1983), 709718.CrossRefGoogle Scholar