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Almost automorphic and weighted pseudo almost automorphic solutions of semilinear evolution equations

Almost automorphic and weighted pseudo almost automorphic solutions of semilinear evolution equations,10.1016/j.jfa.2009.06.007,Journal of Functional

Almost automorphic and weighted pseudo almost automorphic solutions of semilinear evolution equations   (Citations: 7)
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In this paper, applying the theory of semigroups of operators to evolution family and Banach fixed point theorem, we prove the existence and uniqueness of an (a) almost automorphic (weighted pseudo almost automorphic) mild solution of the semilinear evolution equation x′(t)=A(t)x(t)+f(t,x(t)) in Banach space under conditions.
Journal: Journal of Functional Analysis - J FUNCT ANAL , vol. 258, no. 1, pp. 196-207, 2010
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    • ...Recently, the existence and uniqueness of pseudo almost automorphic and weighted almost automorphic mild solutions to differential equations in Banach spaces had attracted many researchers[2-5].The automorphic functions have been applied to many areas include physics, mechanics, dynamical system and mathematical biology...
    • ...Next let us recall some basic results about almost automorphy[2-5]...
    • ...Now, from[5]Lemma 3.1, we know G(t) is an almost automorphic with respect to t.(i.e.G ∈ AA(R, X).)...

    Chou-li Luet al. Weighted Pseudo Almost Automorphic Solution to a Class of Integrodiffe...

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