ON THE EMDEN-FOWLER EQUATION u

doi:10.1016/S0252-9602(10)60119-1

Abstract

Abstract:

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.

Key words: Blow-up, Life-span, Blow-up constant, asymptotic behavior, null

CLC Number:

34A34

LI Ming-Rong. ON THE EMDEN-FOWLER EQUATION u"(t)u(t)=c₁+c₂u' (t)²WITH c₁≥0, c₂ ≥0[J].Acta mathematica scientia,Series B, 2010, 30(4): 1227-1234.

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