Abstract:
Mathematical modelling phenomena of most applied sciences is associated with second order nonlinear differential equations, which are not easily solvable. Therefore, the study of behavior of the solutions has attracted the attention of many mathematicians worldwide. In the present work, we discuss some clear assumptions for the boundedness of all solutions of some non-linear differential equations of second order. The main tools in the proofs of our results are Gronwall's inequality and Bonnet's Theorem. The results obtained here extend and/or improve some of well-known results in the literature. Further, some illustrative examples are provided to show the applicability of the new results
