Electron. J. Diff. Equ.,
Vol. 2014 (2014), No. 236, pp. 115.
Composition of S^pweighted pseudo almost automorphic functions
and applications
ChuanHua Chen, HongXu Li
Abstract:
Since the background space of S^pweighted pseudo almost automorphic
functions (abbr. S^pwpaa functions) is endowed with a norm coming
from L^p norm, it is natural to consider the composition of
S^pwpaa functions under conditions of
L^p norm. However, the known resutls for
composition of S^pwpaa functions were always given under conditions of
supremum norm. Motivated by this, we establish some new results for the
composition of S^palmost automorphic functions and S^pwpaa functions
under a "uniform continuity condition" with respect to L^p norm.
As an application, we prove the existence of mild weighted pseudo almost
automorphic solutions for some semilinear differential equations with
an S^pwpaa force term. An example of the heat equation illustrates
our results.
Submitted September 17, 2014. Published November 06, 2014.
Math Subject Classifications: 43A60, 34G20, 47D03.
Key Words: S^palmost automorphic; uniform continuity;
S^pweighted pseudo almost automorphic;
semilinear differential equation.
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ChuanHua Chen
Department of Mathematics, Sichuan University
Chengdu, Sichuan 610064, China
email: chenchuanhua8@163.com


HongXu Li
Department of Mathematics, Sichuan University
Chengdu, Sichuan 610064, China
email: hoxuli@scu.edu.cn

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