×

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.

MSC:

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

Citations:

Zbl 0958.34050
PDFBibTeX XMLCite
Full Text: DOI

References:

[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.