Nonlinear techniques for linear oscillation problems
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- by Zeev Nehari PDF
- Trans. Amer. Math. Soc. 210 (1975), 387-406 Request permission
Abstract:
It is shown that for differential equations of the form ${y^{(n)}} + py = 0$ there exist associated sets of systems of nonlinear equations which play a role similar to that of the ordinary Riccati equation in the case $n = 2$. In particular, the existence of continuous solutions of the nonlinear system is equivalent to the absence of certain types of oscillatory solutions of the linear equation. If $p$ is of constant sign, the coefficients of the “Riccati systems” are all nonnegative, and the resulting positivity and monotonicity properties make it possible to obtain explicit oscillation criteria for the original equation.References
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Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 210 (1975), 387-406
- MSC: Primary 34C10
- DOI: https://doi.org/10.1090/S0002-9947-1975-0372327-3
- MathSciNet review: 0372327