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Zeitschrift für Analysis und ihre Anwendungen

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Volume 11, Issue 1, 1992, pp. 117–124
DOI: 10.4171/ZAA/621

Published online: 1992-03-31

On a Nonlinear Binomial Equation of Third Order

M. Greguš[1]

(1) Comenius University, Bratislava, Slovak Republic

A necessary and sufficient condition for the solution of equation $u"' + p(t)u^{\alpha} = 0 (\alpha > 0$ an odd integer, $p ≤ 0$ on $(a,\inftly))$ to be oscillatory and some sufficient conditions for the solution in the cases $p ≤ 0$ and $p ≥ 0$ to be oscillatory or non-oscillatory are derived. For this methods and results of the theory of linear differential equations of the third order are effectively used.

Keywords: Third order nonlinear differential equations, oscillatory solutions, non-oscillatory solutions, bounded solutions

Greguš M.: On a Nonlinear Binomial Equation of Third Order. Z. Anal. Anwend. 11 (1992), 117-124. doi: 10.4171/ZAA/621