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

2021 ◽  
Vol 41 (2) ◽  
pp. 413-425
Author(s):  
Yong-Kui Chang ◽  
Yanyan Wei
Keyword(s):  
Periodic Solutions ◽  
Banach Spaces ◽  
Evolution Equations ◽  
Linear Evolution ◽  
Linear Evolution Equations

Periodic Solutions of Non-Linear Evolution Equations in Banach Spaces

1971 ◽  
Vol 23 (1) ◽  
pp. 189-196 ◽  
Author(s):  
Bui An Ton
Keyword(s):  
Periodic Solutions ◽  
Banach Spaces ◽  
Evolution Equations ◽  
Stokes Equations ◽  
Inner Product ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Linear Evolution ◽  
Non Linear ◽  
Linear Evolution Equations

In this paper the theory of Browder [2] and of Lions [3] on periodic solutions of non-linear evolution equations in Banach spaces is put in a more general framework so as to include the Navier-Stokes equations and their variants.An abstract existence theorem is proved in § 1. Applications are given in § 2. The existence of periodic solutions of the Navier-Stokes equations without any restriction on the dimension of the space domain is established. Application of the abstract theorem to the following problem is given:1. Let H be a Hilbert space and (., .)H the inner product in H. Let V and W be two reflexive separable Banach spaces with W ⊂ V ⊂ H. W is dense in V and V is dense in H.

scholarly journals Lumpability of linear evolution Equations in Banach spaces

2017 ◽  
Vol 6 (1) ◽  
pp. 15-34 ◽  
Author(s):  
Fatihcan M. Atay ◽  
◽  
Lavinia Roncoroni ◽  
Keyword(s):  
Banach Spaces ◽  
Evolution Equations ◽  
Linear Evolution ◽  
Linear Evolution Equations

scholarly journals Ulam-Hyers stability and exponentially stable evolution equations in Banach spaces

2021 ◽  
Vol 37 (2) ◽  
pp. 339-344
Author(s):  
ADRIANA BUICĂ
Keyword(s):  
Banach Spaces ◽  
Evolution Equations ◽  
Nonlinear Term ◽  
Lipschitz Constant ◽  
Special Relation ◽  
Linear Evolution ◽  
Exponentially Stable ◽  
Linear Evolution Equations

We show that uniformly exponentially stable abstract linear evolution equations are Ulam-Hyers stable on [a,\infty). Moreover, we prove that this property is maintained when perturbing this type of equations with a nonlinear term having a small Lipschitz constant. These results complement the literature on Ulam-Hyers stability, a special relation having with some works of I. A. Rus.

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