On oscillatory solutions of certain first order ordinary differential equations

Abstract By constructing a class of solutions to the integral inequality α ( t ) ∫ t + ∞ a ( τ ) [ α ( τ ) ] λ d τ for t  ⩾  t 0 large enough, where 0 A 1 ⩽ a ( τ ) ⩽ A 2 + ∞ and λ > 1 , that tend to zero as t → + ∞ we address an open problem in the theory of nonlinear oscillations.