Oscillation theorems for \(n\)th order nonlinear functional differential equations (Q792530)

In six theorems and some corollaries the authors describe the oscillatory behavior of the continuable solutions of the n-th order functional differential equation with a nonlinear damping in the form \[ (a(t)x^{(n-1)})^{\cdot}+p(t)| x^{(n-1)}|^{\beta}x^{(n- 1)}+q(t)f(x[g(t)])=0,\quad \beta \geq 0,\quad n\quad even,\quad q>0. \] Several examples are also introduced and a generalization of the results to the equations of the form \[ (a(t)x^{(n-1)})^{\cdot}+p(t)| x^{(n-1)}|^{\beta}x^{(n-1)}+ \] \[ +f(t,x(t),x[g_ 1(t)],...,x[g_ m(t)])=0,\quad \beta \geq 0,\quad n\quad even, \] is considered.