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

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−2u′)′+g(t,u,u′)u′+a(t)f(u)=e(t),(r(t)|u′|p−2u′)′+g(t,u,u′)u′+a(t)f(u)=e(t), where p>1p>1 is a real constant. The results are applicable to well-known Emden–Fowler and Lienard type equations. An illustrative example is also provided.