Existence and uniqueness of (ω,c)-periodic solutions of semilinear evolution equations

2020 ◽  
Vol 10 (2) ◽  
pp. 149
Author(s):  
Makrina Agaoglou ◽  
Michal Fečkan ◽  
Angeliki P. Panagiotidou
Keyword(s):  
Periodic Solutions ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Semilinear Evolution Equations

scholarly journals Existence of asymptotically periodic solutions for semilinear evolution equations with nonlocal initial conditions

2018 ◽  
Vol 16 (1) ◽  
pp. 792-805
Author(s):  
Junfei Cao ◽  
Zaitang Huang
Keyword(s):  
Periodic Solutions ◽  
Evolution Equations ◽  
Initial Conditions ◽  
Mild Solutions ◽  
Nonlocal Initial Conditions ◽  
Asymptotically Periodic ◽  
Semilinear Evolution Equations ◽  
Asymptotically Periodic Solutions

AbstractIn this paper we study a class of semilinear evolution equations with nonlocal initial conditions and give some new results on the existence of asymptotically periodic mild solutions. As one would expect, the results presented here would generalize and improve some results in this area.

Semilinear evolution equations and fractional powers of a closed pair of operators

1987 ◽  
Vol 105 (1) ◽  
pp. 101-115 ◽  
Author(s):  
Marié Grobbelaar-Van Dalsen
Keyword(s):  
Existence And Uniqueness ◽  
Nonlinear Operator ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Dynamic Boundary Conditions ◽  
Fractional Powers ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Nonlinear Evolution Problem ◽  
Semilinear Evolution Equations

SynopsisThe nonlinear evolution problem [Bu(t)]′ = A(t, Bu)u + f(t, Bu) with B a constant linear operator and A = A(t, Bu) a time-dependent nonlinear operator from one Banach space to another, is studied. Existence and uniqueness results are obtained by making use of the theory of B-evolutions and the fractional powers of A and B. Two examples are presented in which the theory is applied to nonlinear equations with dynamic boundary conditions.

Periodic Solutions for Nonlinear Evolution Equations in RN

2013 ◽  
Vol 860-863 ◽  
pp. 2830-2833
Author(s):  
Li Hong Zhang ◽  
Wei Jie Li
Keyword(s):  
Linear Operator ◽  
Periodic Solutions ◽  
Bounded Linear Operator ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Periodic Problem ◽  
Nonlinear Evolution Equations ◽  
Bounded Linear

The aim of this paper is to establish the existence and uniqueness of periodic solutions for a nonlinear periodic problem: in RN where A(t, x) is a nonlinear map and B is a bounded linear operator from RNto RN .

scholarly journals Periodic Solutions andS-Asymptotically Periodic Solutions to Fractional Evolution Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Jia Mu ◽  
Yong Zhou ◽  
Li Peng
Keyword(s):  
Periodic Solutions ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Fractional Evolution Equations ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Asymptotically Periodic ◽  
Liouville Fractional Derivative ◽  
Asymptotically Periodic Solutions

This paper deals with the existence and uniqueness of periodic solutions,S-asymptotically periodic solutions, and other types of bounded solutions for some fractional evolution equations with the Weyl-Liouville fractional derivative defined for periodic functions. Applying Fourier transform we give reasonable definitions of mild solutions. Then we accurately estimate the spectral radius of resolvent operator and obtain some existence and uniqueness results.

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