Taylor, W. E. jun. Oscillation criteria for certain nonlinear fourth order equations. (English) Zbl 0539.34021 Int. J. Math. Math. Sci. 6, 551-557 (1983). The author considers the following equation: (1) \(y^{(4)}+p(t)y'+q(t)f(y)=0\), where (i) p’,q,r are continuous functions on \([0,\infty)\) and \(p(t)>0\), \(q(t)>0\) on \([0,\infty)\), f is continuous on R and \(f(y)/y\geq m>0\) for \(y\neq 0\); (ii) \(mq-p'\geq 0\) on \([o,\infty)\). (2) \(y^{(4)}+p(t)y'+q(t)f(y)=r(t),\) where (i) and \(p'(t)<0\) on \([0,\infty)\), \(\int^{\infty}(r^ 2(t)/p'(t))dt>-\infty\) hold. Under these and other assumptions he establishes several criteria for the existence of oscillatory solutions of (1) and (2). Reviewer: P.Marusiak Cited in 3 Documents MSC: 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems 34E05 Asymptotic expansions of solutions to ordinary differential equations Keywords:nonlinear fourth order equations; asymptotic behavior; criteria; oscillatory solutions PDFBibTeX XMLCite \textit{W. E. Taylor jun.}, Int. J. Math. Math. Sci. 6, 551--557 (1983; Zbl 0539.34021) Full Text: DOI EuDML