Department of Mathematics, Sichuan University
Chengdu, Sichuan 610064, China
email: chenchuanhua8@163.com
Department of Mathematics, Sichuan University
Chengdu, Sichuan 610064, China
email: hoxuli@scu.edu.cn
Chuan-Hua Chen, Hong-Xu Li
Abstract:
Since the background space of S^p-weighted pseudo almost automorphic
functions (abbr. S^p-wpaa functions) is endowed with a norm coming
from L^p norm, it is natural to consider the composition of
S^p-wpaa functions under conditions of
L^p norm. However, the known resutls for
composition of S^p-wpaa functions were always given under conditions of
supremum norm. Motivated by this, we establish some new results for the
composition of S^p-almost automorphic functions and S^p-wpaa 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^p-wpaa 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^p-almost automorphic; uniform continuity;
S^p-weighted pseudo almost automorphic;
semilinear differential equation.
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Chuan-Hua Chen Department of Mathematics, Sichuan University Chengdu, Sichuan 610064, China email: chenchuanhua8@163.com |
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Hong-Xu Li Department of Mathematics, Sichuan University Chengdu, Sichuan 610064, China email: hoxuli@scu.edu.cn |
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