Pseudo almost automorphic and weighted pseudo almost automorphic mild solutions to a partial functional differential equation in Banach spaces

Chang, Yong-Kui¹ ; Zhao, Zhi-Han² ; Nieto, Juan J.³ ; Liu, Zhi-Wei⁴

¹ Department of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, Ginsu, China
² Institute of Mathematics and Information Engineering, Sanming University, Sanming,365004, Fujian, China
³ Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, Santiago de Compostela, 15782, Spain
⁴ Department of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China

Journal of nonlinear sciences and its applications, Tome 5 (2012) no. 1, p. 14-26.

Résumé

In this paper we prove some existence and uniqueness results for pseudo almost automorphic and weighted pseudo almost automorphic mild solutions to a class of partial functional differential equation in Banach spaces. The main technique is based upon some appropriate composition theorems combined with the Banach contraction mapping principle and fractional powers of operators.

Détail

DOI : 10.22436/jnsa.005.01.02

Classification : 44A35, 42A85, 42A75
Keywords: Pseudo almost automorphic, Weighted pseudo almost automorphic, Partial functional differential equations, Fractional powers of operators.

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