Oscillation criteria for certain nonlinear fourth order equations. (English) Zbl 0539.34021

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


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
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