BLOW-UP RESULTS AND ASYMPTOTIC BEHAVIOR OF THE EMDEN-FOWLER EQUATION u＂ = ｜u｜^p

In this article the author works with the ordinary differential equation u＂ = ｜u｜^p for some p 〉 0 and obtains some interesting phenomena concerning blow-up, blow-up rate, life-span, stability, instability, zeros and critical points of solutions to this equation.     

QUENCHING PROBLEM IN SOME SEMILINEAR WAVE EQUATIONS

This article proves a quenching result of the solutions for some semi-linear wave equations.     

BLOW-UP RESULTS AND ASYMPTOTIC BEHAVIOR OF THE EMDEN-FOWLER EQUATION u″=|u|~p

In this article the author works with the ordinary differential equation u″= |u|~p for some p>0 and obtains some interesting phenomena concerning blow-up,blow-up rate,life-span,stability,instability,zeros and critical points of solutions to this equation.     

ON THE EMDEN-FOWLER EQUATION u″（t）u（t） = c1＋c2u′（t）^2 WITH c1≥0, c2≥0

In this article, we study the following initial value problem for the nonlinear equation
{u″u（t）=c1＋c2u′（t）^2, c1≥0, c2≥0,
u（0）=u0, u′（0）=u1.
We are interested in properties of solutions of the above problem. We find the life-span, blow-up rate, blow-up constant and the regularity, null point, critical point, and asymptotic behavior at infinity of the solutions.