Geodesic
Dependence results on almost periodic and almost automorphic solutions of evolution equations
Electronic journal of differential equations, Tome 2010 (2010)
We consider the semilinear evolution equations $x'(t) = A(t) x(t) + f(x(t), u(t),t)$ and $x'(t) = A(t) x(t) + f(x(t), \zeta,t)$ where $A(t)$ is a unbounded linear operator on a Banach space X and f is a nonlinear operator. We study the dependence of solutions x with respect to the function $u$ in three cases: the continuous almost periodic functions, the differentiable almost periodic functions, and the almost automorphic functions. We give results on the continuous dependence and on the differentiable dependence.
Classification : 47J35, 43A60, 47D06
Keywords: semilinear evolution equation, almost periodic function, almost automorphic function, dependence results 
@article{EJDE_2010__2010__a45,
     author = {Blot,  Joel and Cieutat,  Philippe and N'Guerekata,  Gaston M.},
     title = {Dependence results on almost periodic and almost automorphic solutions of evolution equations},
     journal = {Electronic journal of differential equations},
     year = {2010},
     volume = {2010},
     zbl = {1201.47076},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a45/}
}
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AU  - Cieutat,  Philippe
AU  - N'Guerekata,  Gaston M.
TI  - Dependence results on almost periodic and almost automorphic solutions of evolution equations
JO  - Electronic journal of differential equations
PY  - 2010
VL  - 2010
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LA  - en
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%A N'Guerekata,  Gaston M.
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%J Electronic journal of differential equations
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%V 2010
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%G en
%F EJDE_2010__2010__a45
Blot,  Joel; Cieutat,  Philippe; N'Guerekata,  Gaston M. Dependence results on almost periodic and almost automorphic solutions of evolution equations. Electronic journal of differential equations, Tome 2010 (2010). http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a45/