Solutions to abstract integral equations and infinite delay evolution equations
نویسندگان
چکیده
منابع مشابه
Stability of solutions to abstract evolution equations with delay
An equation u̇ = A(t)u+B(t)F (t, u(t−τ)), u(t) = v(t),−τ ≤ t ≤ 0 is considered, A(t) and B(t) are linear operators in a Hilbert space H, u̇ = du dt , F : H → H is a non-linear operator, τ > 0 is a constant. Under some assumption on A(t), B(t) and F (t, u) sufficient conditions are given for the solution u(t) to exist globally, i.e, for all t ≥ 0, to be globally bounded, and to tend to zero at a s...
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For A(t) and f (t, x, y) T -periodic in t , we consider the following evolution equation with infinite delay in a general Banach space X: u′(t)+A(t)u(t)= f (t, u(t), ut ), t > 0, u(s)= φ(s), s 0, (0.1) where the resolvent of the unbounded operator A(t) is compact, and ut (s) = u(t + s), s 0. By utilizing a recent asymptotic fixed point theorem of Hale and Lunel (1993) for condensing operators t...
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In this paper we apply the technique of measures of noncompactness to the theory of infinite system of integral equations in the Fr´echet spaces. Our aim is to provide a few generalization of Tychonoff fixed point theorem and prove the existence of solutions for infinite systems of nonlinear integral equations with help of the technique of measures of noncompactness and a generalization of Tych...
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ژورنال
عنوان ژورنال: Bulletin of the Belgian Mathematical Society - Simon Stevin
سال: 2011
ISSN: 1370-1444
DOI: 10.36045/bbms/1323787167