New oscillation criteria for nonlinear delay differential equations of fourth-order

摘要

By using a generalized Riccati substitution, we present a new criterion for oscillation of solutions of fourth-order quasi-linear differential equations (r(t)(x‴(t))α)′ + f(t,x(σ(t)))=0, in noncanonical case ∫∞r−1/α(s)ds  < ∞. We utilize an approach that gives rise to two or three independent conditions, eliminating non-oscillatory solutions. Moreover, we establish conditions in a non-traditional form (limsup(·)>1), while condition (limsup(·)=∞) cannot be applied. Our results essentially improve and complement a number of related ones. Examples are provided to illustrate the results.