Uncountably many nonoscillatory bounded solutions to second-order nonlinear neutral dynamic equations

Abstract

This work is devoted to the study of the existence of uncountably many nonoscillatory bounded solutions tosecond-order nonlinear neutral dynamic equations by means of the Darbo fixed point theorem. We construct assumptionswithout sign conditions on the nonlinear part of the equation. Moreover, we prove the necessary condition for the existenceof an asymptotically zero solution to the problem under consideration.