Remarks on the existence of nonoscillatory solutions of half-linear ordinary differential equations, II

Abstract

We consider the half-linear differential equation of the form (p(t)|x′|αsgnx′)′ + q(t)|x|sgnx = 0 , t ≥ t0 , under the assumption that p(t)−1/α is integrable on [t0,∞). It is shown that if a certain condition is satisfied, then the above equation has a pair of nonoscillatory solutions with specific asymptotic behavior as t→∞.