Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Oscillation and nonoscillation of solutions of generalized Emden-Fowler equations

Authors: C. V. Coffman and J. S. W. Wong
Journal: Trans. Amer. Math. Soc. 167 (1972), 399-434
MSC: Primary 34C10
MathSciNet review: 0296413
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: This paper treats the ordinary differential equation $ y'' + yF({y^2},x) = 0,x > 0$ , where $ yF({y^2},x)$ is continuous in (y, x) for $ x > 0,\vert y\vert < \infty $, and $ F(t,x)$ is non-negative; the equation is assumed to be either of sublinear or superlinear type. Criteria are given for the equation to be oscillatory, to be nonoscillatory, to possess oscillatory solutions or to possess nonoscillatory solutions. An attempt has been made to unify the methods of treatment of the sublinear and superlinear cases. These methods consist primarily of comparison with linear equations and the use of ``energy'' functions. An Appendix treats the questions of continuability and uniqueness of solutions of the equation considered in the main text.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 34C10

Retrieve articles in all journals with MSC: 34C10

Additional Information

Keywords: Oscillation, nonoscillation, nonlinear
Article copyright: © Copyright 1972 American Mathematical Society

American Mathematical Society