S-Asymptotically Bloch Type Periodic Solutions to Some Semi-Linear Evolution Equations in Banach Spaces

Pseudo $ S $-asymptotically Bloch type periodic solutions to a damped evolution equation

“…The aim of this paper is to investigate the existence of pseudo S-asymptotically Bloch type periodic mild solutions to (1) by introducing pseudo S-asymptotically Bloch type periodic function on R + . Our results can be considered as a useful supplement to the works [1,2,10,11]. It should be pointed out that few results are available yet for the existence of pseudo S-asymptotically ω-anti-periodic solutions to (1) since the notion of pseudo S-asymptotically ω-anti-periodic function on the nonnegative real axis is not specially mentioned up to now.…”

Weighted pseudo S-asymptotically Bloch type periodic solutions for a class of mean field stochastic fractional evolution equations

“…Some publications have also explored the effects of perturbations on Bloch periodic functions, by defining some quasi-Bloch periodicity concepts. For instance, [18,20,32] studied asymptotically Bloch periodic functions and their applications, while [31][32][33][34] investigated (pseudo) S-asymptotically Bloch periodic functions and their applications. These quasi-Bloch periodic functions are extensions of the corresponding asymptotically ω-periodic and (pseudo) S-asymptotically ω-periodic functions in the deterministic case.…”

“…Moreover, if f ≡ 0 and g(t, v(t), P v(t) ) ≡ g(t, v(t)), the existence and uniqueness of almost automorphic, asymptotically periodic, almost periodic, asymptotically ω-periodic solutions, S-asymptotically ω-periodic solutions, asymptotically almost periodic and asymptotically almost automorphic, (ω, c)-periodic and pseudo S-asymptotically (ω, k)-Bloch periodic mild solutions of problem (1.1) have been investigated in deterministic cases by various authors [6,8,9,24,35,36,38]. In this work, the problem (1.1) captures fading memory behaviors, and randomness of the dynamical processes.…”

Besicovitch Almost Periodic Solutions of Abstract Semi-Linear Differential Equations with Delay

“…On the other hand, it is well known that the existence of periodic solutions and almost periodic solutions is one of the important research contents of the qualitative theory of differential equations, see in [13][14][15][16][17][18][19][20][21][22] and the references therein. Nevertheless, there are still few results on the existence of Besicovitch almost periodic solutions for differential equations [23].…”