On the existence and asymptotic behavior of the random solutions of the random integral equation with advancing argument
Henryk Gacki
Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 16 (1996), p. 43-51 / Harvested from The Polish Digital Mathematics Library
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1. Introduction Random Integral Equations play a significant role in characterizing of many biological and engineering problems [4,5,6,7]. We present here new existence theorems for a class of integral equations with advancing argument. Our method is based on the notion of a measure of noncompactness in Banach spaces and the fixed point theorem of Darbo type. We shall deal with random integral equation with advancing argument x(t,ω)=h(t,ω)+∫t+δ(t)₀k(t,τ,ω)f(τ,xτ(ω))dτ, (t,ω) ∈ R⁺ × Ω, (1) where (i) (Ω,A,P) is a complete probability space, (ii) x = x(t,ω) denotes an unknown random function defined for t ∈ R⁺ and ω ∈ Ω, (iii) δ is a nonnegative function from R⁺ into R⁺, (iv) xₜ(ω) denotes the restriction of the function x(t,ω) to the interval [0,t+δ(t)], t>0, with x₀(ω) = x(0,ω) ∈ L²(Ω,A,P).

Publié le : 1996-01-01
EUDML-ID : urn:eudml:doc:275950 
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Henryk Gacki. On the existence and asymptotic behavior of the random solutions of the random integral equation with advancing argument. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 16 (1996) pp. 43-51. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-div16i1n2bwm/

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