μ-Pseudo Almost Periodic and Automorphic Solutions in the α-Norm for Some Partial Functional Differential Equations

Abstract

In this work, we prove the existence and uniqueness of -pseudo almost periodic andpseudo almost automorphic solutions in the −norm for some classes of partial differential equations in Banach spaces. For illustration, we study some models arising in physical systems.

Dynamics and oscillations of models for differential equations with delays

“…The notion of measure pseudo almost periodicity was first introduced by Blot et al [5] (see also [1,8,12,13,15,16,17,27]). Obviously, these new results generalize the earlier work od Diagana [10].…”

On the integro‐differential equations with reflection

“…1 For more details on these last themes, one can read the two references of Veech 2 and N'Guérékata. 3 The notion of measure pseudo almost periodicity and automorphy [4][5][6][7][8][9][10][11][12] is a generalization of pseudo periodicity and weighted periodicity (see the literature 13,14 ).…”

Strongly damped wave equations with Stepanov type nonlinear forcing term

“…Recently, Xia et al in [22] introduced and investigated the (μ, ν)-pseudo S-asymptotically ω-periodic functions of class r and gave some applications. For related works, see [8,13,21] and the references therein.…”

“…12)f aa (t + τ , ϕ 1 , ϕ 2 )f aa (t, ϕ 1 , ϕ 2 ) L p ( ) ≤ |μ| a(t + τ )a(t) × h e (ϕ 1 ) L ∞ ( ) + g e (ϕ 1 ) L ∞ ( ) ϕ 1 H 2 p ( ) C|μ| a(t + τ )a(t) ( ) ϕ 1 H 2 p ( ) ≤ C(K) a(t + τ )a(t) ,(4 13). …”