Oscillation of certain third order functional differential equations. (English) Zbl 1116.34050

The authors consider third order functional differential equations of the form \[ L_{3}x(t)+\delta q(t)f(x[g(t)])=0, \] where \(\delta=\pm 1\), \(L_{0}x(t)=x(t)\), \(L_{3}x(t)=\frac{d}{dt}L_{2}x(t)\), \(L_{k}x(t)={1\over a_{k}(t)}\left(\frac{d}{dt}L_{k-1}x(t)\right)^{\alpha_{k}}, k=1, 2\). By discussing the nonexistence of some types of solutions to the above equations, they establish a number of new oscillation criteria for these equations. They also give three illustrative examples and apply the previous results to neutral equations of the form \[ L_{3}(x(t)+p(t)x[\tau(t)])+\delta q(t)f(x[g(t)])=0. \]


34K11 Oscillation theory of functional-differential equations