On positive solutions of perturbed nonlinear differential equations

Some results are given concerning positive solutions of equations of the form x⁽ⁿ⁾ + P(t) G(x) = Q(t, x).Let class I (II) consist of all n-times differentiable functions x(t), such that x(t)>0 and x^{(n ? 1)}(t) ? 0 (x^{(n ? 1)}(t) ? 0) for all large t. Two theorems are given guaranteeing the nonexistence of solutions in class I and II, respectively, and three theorems ensure the convergence to zero of positive solutions. A recent result of Hammett concerning the second-order case is extended to the general case.