Oscillation criteria for certain nonlinear fourth order equations (Q793891)

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).