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S. Boulite L. Maniar G. M. N'Gué ré kata 《Proceedings of the American Mathematical Society》2006,134(12):3613-3624
In this work, we use the extrapolation methods to study the existence and uniqueness of almost automorphic solutions to the semilinear boundary differential equation
where generates a hyperbolic -semigroup on a Banach space and are almost automorphic functions which take values in and a ``boundary space' , 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.
where generates a hyperbolic -semigroup on a Banach space and are almost automorphic functions which take values in and a ``boundary space' , 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.
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Existence of $\mu$-pseudo almost automorphic solutions to abstract partial neutral functional differential equations with infinite delay
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Yong-Kui Chang G. M. N''Gu ''{e}r ''{e}kat Rui Zhang 《Journal of Applied Analysis & Computation》2016,6(3):628-664
In this article, we introduce and investigate the concept of $\mu$-Stepanov-like pseudo almost automorphic functions of class $h$ and class infinity via measure theory. We present new results on completeness and composition theorems for the space of such functions. To illustrate our main results, we provide some applications to an abstract partial neutral functional differential equation with infinite delay. 相似文献
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J. Q. Zhao Y. K. Chang G. M. N’Guérékata 《Journal of Optimization Theory and Applications》2013,156(1):106-114
This paper is mainly concerned with the asymptotically almost automorphic mild solutions to a semilinear fractional differential equation. Some asymptotic behavior of mild solutions to this equation has been established by properties and composition theorems of asymptotically almost automorphic functions and fixed point theorems. 相似文献
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Hui-Sheng Ding Jin Liang Gaston M. N’Guérékata Ti-Jun Xiao 《Nonlinear Analysis: Theory, Methods & Applications》2008
This paper is concerned with neutral nonlinear delay integral equations. We establish an existence theorem for positive almost automorphic solutions to the equations, which extend some existing results even in the case of almost periodicity. Some examples are given to illustrate our results. 相似文献
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Hui-Sheng Ding Yuan-Yuan Chen Gaston M. N’Guérékata 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(18):7356-7364
In this work, a new fixed point theorem in partially ordered Banach spaces is established, and then used to prove the existence of positive pseudo almost periodic solutions to a class of neutral integral equations. Our existence theorem extends some recent results due to [E. Ait Dads, P. Cieutat, L. Lhachimi, Positive pseudo almost periodic solutions for some nonlinear infinite delay integral equations, Mathematical and Computer Modelling 49 (2009) 721–739] to a more general class of integral equations. 相似文献