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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

##### 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
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