Global existence and boundedness for a class of second-order nonlinear differential equations

Abstract

In this paper we obtain new conditions for the global existence and boundedness of solutions for nonlinear second-order equations of the form ( r ( t ) | u ′ | p − 2 u ′ ) ′ + g ( t , u , u ′ ) u ′ + a ( t ) f ( u ) = e ( t ) , where p > 1 is a real constant. The results are applicable to well-known Emden–Fowler and Lienard type equations. An illustrative example is also provided.