Almost automorphic solutions for semilinear boundary differential equations
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- by S. Boulite, L. Maniar and G. M. N’Guérékata PDF
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Abstract:
In this work, we use the extrapolation methods to study the existence and uniqueness of almost automorphic solutions to the semilinear boundary differential equation \begin{equation} \tag {SBDE} \left \{ \begin {aligned} x’(t) &= A_mx(t)+h(t,x(t)), && t\in \mathbb {R}, \\ Lx(t) &= g(t,x(t)), && t\in \mathbb {R}, \end{aligned} \right . \end{equation} where $A:=A_m|\ker L$ generates a hyperbolic $C_0$-semigroup on a Banach space $X$ and $h,g$ are almost automorphic functions which take values in $X$ and a “boundary space” $\partial X$, respectively. These equations are an abstract formulation of partial differential equations with semilinear terms at the boundary, such as population equations, retarded differential equations and boundary control systems. An application to retarded differential equations is given.References
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Additional Information
- S. Boulite
- Affiliation: Department of Mathematics, Faculty of Sciences Semlalia, B.P. 2390, Marrakesh, Morocco
- Email: sboulite@ucam.ac.ma
- L. Maniar
- Affiliation: Department of Mathematics, Faculty of Sciences Semlalia, B.P. 2390, Marrakesh, Morocco
- Email: maniar@ucam.ac.ma
- G. M. N’Guérékata
- Affiliation: Department of Mathematics, Morgan State University, 1700 E. Cold Spring Lane, Baltimore, Maryland 21251
- ORCID: 0000-0001-5765-7175
- Email: gnguerek@morgan.edu.
- Received by editor(s): June 13, 2005
- Received by editor(s) in revised form: July 6, 2005
- Published electronically: June 12, 2006
- Communicated by: Carmen C. Chicone
- © Copyright 2006 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 134 (2006), 3613-3624
- MSC (2000): Primary 34A05, 34G20, 47A55
- DOI: https://doi.org/10.1090/S0002-9939-06-08423-1
- MathSciNet review: 2240674