A FIXED POINT APPROACH OF THE ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR DIFFERENTIAL EQUATIONS OF SECOND ORDER

Abstract

 In an adecquate Banach space the integral operator associated to the initial value problem u''+f(t,u,u')=0, t³t₀, u(t₀)=U₀, u'(t₀)=U₁ for some t₀³1 (for simplicity) satisfies the requirements of the Schauder-Tychonov theorem if f(t,u,v) is under a Bihari type restriction. The fixed point u(t) of this operator is asymptotic to at+b as t®+¥, where a, b are real constants.