Forced oscillation of \(n\)th-order nonlinear differential equations. (English) Zbl 1033.34046

Summary: The oscillation criteria result of R. P. Agarwal and S. R. Grace [ Appl. Math. Lett. 13, 53–57 (2000; Zbl 0958.34050)] is generalized to the following nonlinear equations \[ x^{(n)}(t)+ \sum^{n-1}_{i=1} a_i x^{(i)}(t)- q(t) f(x(t))= e(t),\quad n\in\mathbb{N}, \] where \(f\in C^1(\mathbb{R},\mathbb{R})\) and \(f\) is a strictly monotone increasing function, \(e\in C(\mathbb{R}^+,\mathbb{R})\) and \(a_1,\dots, a_{n-1}\) are real constants.


34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations


Zbl 0958.34050
Full Text: DOI


[1] Agarwal, R. P.; Grace, S. R., Forced oscillation of \(n\) th-order nonlinear differential equations, Appl. Math. Lett., 13, 53-57 (2000) · Zbl 0958.34050
[2] Hardy, G. H.; Littlewood, J. E.; Polya, G., Inequalities (1988), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0634.26008
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