Opuscula Math. 31, no. 3 (2011), 457-474
http://dx.doi.org/10.7494/OpMath.2011.31.3.457
Opuscula Mathematica
A new composition theorem for Sp-weighted pseudo almost periodic functions and applications to semilinear differential equations
Zhi-Han Zhao
Yong-Kui Chang
G. M. N'Guérékata
Abstract. In this paper, we establish a new composition theorem for \(S^p\)-weighted pseudo almost periodic functions under weaker conditions than the Lipschitz ones currently encountered in the literatures. We apply this new composition theorem along with the Schauder's fixed point theorem to obtain new existence theorems for weighted pseudo almost periodic mild solutions to a semilinear differential equation in a Banach space.
Keywords: \(S^p\)-weighted pseudo almost periodic, weighted pseudo almost periodicity, semilinear differential equations.
Mathematics Subject Classification: 34K14, 60H10, 35B15, 34F05.
- Zhi-Han Zhao
- Lanzhou Jiaotong University, Department of Mathematics, Lanzhou, Gansu 730070, P.R. China
- Yong-Kui Chang
- Lanzhou Jiaotong University, Department of Mathematics, Lanzhou, Gansu 730070, P.R. China
- G. M. N'Guérékata
- Morgan State University, Department of Mathematics, 1700 E. Cold Spring Lane, Baltimore, M.D. 21251, USA
- Received: 2010-12-04.
- Accepted: 2011-01-04.
