Measure pseudoasymptotically Bloch periodic functions in the sense of Stepanov and their applications (Q6633997)

In this wok, the authors introduced a new class of ergodicunctions, namely, the Stepanov-like pseudo asymptotically Bloch-periodicity in Stepanov sense. The authors used the measure approach to define the space of pseudo asymptotically Bloch-periodic functions. Then, they proved several properties of that space, like the completeness. The main results are applied to some nonlinear partial functional differential equations. The linear part is assumed to generate an exponentially stable co-semigroup on a Banach space. The input function is assumed to be Stepanov-Like Pseudoasymptotically Bloch-Periodic. The authors used the Banach's fixed point theorem to prove the existence and uniqueness of a Stepanov-Like Pseudoasymptotically Bloch-Periodic Solutions for the nonlinear system. An application is provided for some reaction-diffusion equation with delay.