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

DOI:
https://doi.org/10.1090/S0002-9947-1972-0296413-9

MathSciNet review:
0296413

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Abstract | References | Similar Articles | Additional Information

Abstract: This paper treats the ordinary differential equation , where is continuous in (*y, x*) for , and 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.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1972-0296413-9

Keywords:
Oscillation,
nonoscillation,
nonlinear

Article copyright:
© Copyright 1972
American Mathematical Society