On the continuation and boundedness of solutions of a nonlinear differential equation

AbstractSufficient conditions are given so that all solutions of the nonlinear differential equation u″ + φ(t, u, u′)u′ + p(t) gf(u) g(u′) = h(t, u, u′) are continuable to the right of an initial t-value t0 ⩾ 0. These conditions are then extended so that all solutions u of the equation in question together with their derivative u′ are bounded for t ⩾ t0