Blow-up solutions of nonlinear differential equations

We consider the initial value problems for second order nonlinear differential equations of the form∣u′∣m-2u′′=upand the systemui″=fi(u1,u2),i=1,2.By using the energy method, some blow-up properties such as the life span, blow-up rates and blow-up constants are given and the asymptotic behavior of the global solution is also discussed.