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Weighted Stepanov-like pseudo almost automorphy and applications. (English) Zbl 1306.35140

Summary: We propose a new class of functions called weighted Stepanov-like pseudo almost automorphic functions, which generalize in a natural fashion the concept of almost automorphy and its various extensions. We systematically explore the properties of the weighted Stepanov-like pseudo almost automorphic functions in general Banach space including a composition result. As an application, we establish some sufficient criteria for the existence, uniqueness of the weighted pseudo almost automorphic solution to a class of partial neutral functional differential equations and also to a class of nonlinear Volterra integral equations of convolution type with infinite delay in Banach space. Some interesting examples are presented to illustrate the main findings.

MSC:

35R20 Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions)
35R10 Partial functional-differential equations
45D99 Volterra integral equations
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