Oscillation and nonoscillation of solutions of generalized Emden-Fowler equations

Coffman, C. V.; Wong, J. S. W.

doi:10.1090/S0002-9947-1972-0296413-9

Oscillation and nonoscillation of solutions of generalized Emden-Fowler equations
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by C. V. Coffman and J. S. W. Wong

Trans. Amer. Math. Soc. 167 (1972), 399-434

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

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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 $x > 0,|y| < \infty$, 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.

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