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

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.

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Periodic Solutions andS-Asymptotically Periodic Solutions to Fractional Evolution Equations

Discrete Dynamics in Nature and Society ◽

10.1155/2017/1364532 ◽

2017 ◽

Vol 2017 ◽

pp. 1-12 ◽

Cited By ~ 3

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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Existence of positive S-asymptotically periodic solutions of the fractional evolution equations in ordered Banach spaces

Nonlinear Analysis Modelling and Control ◽

10.15388/namc.2021.26.24176 ◽

2021 ◽

Vol 26 (5) ◽

pp. 928-946

Author(s):

Qiang Li ◽

Lishan Liu ◽

Mei Wei

Keyword(s):

Evolution Equations ◽

Mild Solutions ◽

Upper And Lower Solutions ◽

Periodic Problem ◽

Growth Conditions ◽

Monotone Iterative Method ◽

Monotone Iterative ◽

Asymptotically Periodic ◽

Asymptotically Periodic Solutions ◽

Ordered Banach Spaces

In this paper, we discuss the asymptotically periodic problem for the abstract fractional evolution equation under order conditions and growth conditions. Without assuming the existence of upper and lower solutions, some new results on the existence of the positive S-asymptotically ω-periodic mild solutions are obtained by using monotone iterative method and fixed point theorem. It is worth noting that Lipschitz condition is no longer needed, which makes our results more widely applicable.

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Nonlocal problem for fractional stochastic evolution equations with solution operators

Fractional Calculus and Applied Analysis ◽

10.1515/fca-2016-0078 ◽

2016 ◽

Vol 19 (6) ◽

Cited By ~ 5

Author(s):

Pengyu Chen ◽

Xuping Zhang ◽

Yongxiang Li

Keyword(s):

Hilbert Spaces ◽

Evolution Equations ◽

Initial Conditions ◽

Mild Solutions ◽

Nonlocal Problem ◽

Growth Conditions ◽

Stochastic Evolution ◽

Stochastic Evolution Equations ◽

Nonlocal Initial Conditions ◽

Analysis Theory

AbstractIn this article, we are concerned with a class of fractional stochastic evolution equations with nonlocal initial conditions in Hilbert spaces. The existence of mild solutions is obtained under the situation that the nonlinear term satisfies some appropriate growth conditions by using fractional calculations, Schauder fixed point theorem, stochastic analysis theory,

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Existence of Solutions in Some Interpolation Spaces for a Class of Semilinear Evolution Equations with Nonlocal Initial Conditions

Journal of Function Spaces and Applications ◽

10.1155/2013/451252 ◽

2013 ◽

Vol 2013 ◽

pp. 1-11

Author(s):

Jung-Chan Chang ◽

Hsiang Liu

Keyword(s):

Evolution Equations ◽

Existence Of Solutions ◽

Initial Conditions ◽

Linear Part ◽

Nonlocal Conditions ◽

Strong Solutions ◽

Interpolation Spaces ◽

Nonlocal Initial Conditions ◽

Densely Defined ◽

Semilinear Evolution Equations

This paper is concerned with the existence of mild and strong solutions for a class of semilinear evolution equations with nonlocal initial conditions. The linear part is assumed to be a (not necessarily densely defined) sectorial operator in a Banach spaceX. Considering the equations in the norm of some interpolation spaces betweenXand the domain of the linear part, we generalize the recent conclusions on this topic. The obtained results will be applied to a class of semilinear functional partial differential equations with nonlocal conditions.

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