scholarly journals Doss ρ-Almost Periodic Type Functions in Rn

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2825
Author(s):  
Marko Kostić ◽  
Wei-Shih Du ◽  
Vladimir E. Fedorov
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Banach Spaces ◽  
Binary Relation ◽  
General Setting ◽  
Translation Invariance ◽  
Variable Exponents ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Lebesgue Spaces

In this paper, we investigate various classes of multi-dimensional Doss ρ-almost periodic type functions of the form F:Λ×X→Y, where n∈N, ∅≠Λ⊆Rn,X and Y are complex Banach spaces, and ρ is a binary relation on Y. We work in the general setting of Lebesgue spaces with variable exponents. The main structural properties of multi-dimensional Doss ρ-almost periodic type functions, like the translation invariance, the convolution invariance and the invariance under the actions of convolution products, are clarified. We examine connections of Doss ρ-almost periodic type functions with (ω,c)-periodic functions and Weyl-ρ-almost periodic type functions in the multi-dimensional setting. Certain applications of our results to the abstract Volterra integro-differential equations and the partial differential equations are given.

scholarly journals Almost periodic and asymptotically almost periodic type functions in Lebesgue spaces with variable exponents Lp(x)

Filomat ◽  
2020 ◽  
Vol 34 (5) ◽  
pp. 1629-1644
Author(s):  
Toka Diagana ◽  
Marko Kostic
Keyword(s):  
Differential Equations ◽  
Banach Spaces ◽  
Almost Periodic Functions ◽  
Important Class ◽  
Variable Exponents ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Lebesgue Spaces ◽  
Asymptotically Almost Periodic

In this paper we introduce and analyze an important class of (asymptotically) Stepanov almost periodic functions in the Lebesgue spaces with variable exponents, which generalizes in a natural fashion all the (asymptotically) almost periodic functions. We then make extensive use of these new functions to study some abstract Volterra integro-differential equations in Banach spaces including multi-valued ones.

scholarly journals Generalized Almost Periodicity in Lebesgue Spaces with Variable Exponents

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 928 ◽  
Author(s):  
Marko Kostić ◽  
Wei-Shih Du
Keyword(s):  
Banach Spaces ◽  
Differential Inclusions ◽  
Almost Periodic Functions ◽  
Almost Periodicity ◽  
Variable Exponents ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Lebesgue Spaces ◽  
Recurrent Functions ◽  
Convolution Products

In this paper, we introduce and analyze Stepanov uniformly recurrent functions, Doss uniformly recurrent functions and Doss almost-periodic functions in Lebesgue spaces with variable exponents. We investigate the invariance of these types of generalized almost-periodicity in Lebesgue spaces with variable exponents under the actions of convolution products, providing also some illustrative applications to the abstract semilinear integro-differential inclusions in Banach spaces.

scholarly journals Generalized Almost Periodicity in Lebesgue Spaces with Variable Exponents, Part II

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1052
Author(s):  
Marko Kostić ◽  
Wei-Shih Du
Keyword(s):  
Banach Spaces ◽  
Differential Inclusions ◽  
Variable Exponent ◽  
Almost Periodicity ◽  
Variable Exponents ◽  
Almost Periodic ◽  
Fractional Differential Inclusions ◽  
Lebesgue Spaces ◽  
Fractional Differential ◽  
Recurrent Type

In this paper, we introduce and analyze several different notions of almost periodic type functions and uniformly recurrent type functions in Lebesgue spaces with variable exponent L p ( x ) . We primarily consider the Stepanov and Weyl classes of generalized almost periodic type functions and generalized uniformly recurrent type functions. We also investigate the invariance of generalized almost periodicity and generalized uniform recurrence with variable exponents under the actions of convolution products, providing also some illustrative applications to the abstract fractional differential inclusions in Banach spaces.

scholarly journals Rhythm Drivers, Physical Properties, Mechanisms of Formation

2021 ◽  
Vol 248 ◽  
pp. 01007
Author(s):  
Mikhail Mazurov
Keyword(s):  
Mathematical Model ◽  
Partial Differential Equations ◽  
Nonlinear System ◽  
Differential Equations ◽  
Physical Properties ◽  
Ordinary Differential Equations ◽  
Numerical Study ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Mechanisms Of Formation

A mathematical model of the pacemaker is presented in the form of a nonlinear system of ordinary differential equations and in the form of a system of partial differential equations for distributed pacemakers. For the numerical study of the properties of the pacemaker, a modified axiomatic Wiener-Rosenbluth method was used using the properties of uniform almost periodic functions. Physical foundations, mechanisms of formation, properties of point and distributed pacemakers are described in detail.

scholarly journals On some classes of almost periodic functions in abstract spaces

2004 ◽  
Vol 2004 (61) ◽  
pp. 3237-3247 ◽  
Author(s):  
Dariusz Bugajewski ◽  
Gaston M. N'Guérékata
Keyword(s):  
Banach Space ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Superposition Operator ◽  
Periodic Functions ◽  
Partial Differential ◽  
Abstract Spaces

We deal withC(n)-almost periodic functions taking values in a Banach space. We give several properties of such functions, in particular, we investigate their behavior in view of differentiation as well as integration. The superposition operator acting in the space of such functions is also under consideration. Some applications to ordinary as well as partial differential equations are presented. Moreover, we introduce the class of the so-called asymptoticallyC(n)-almost periodic functions and give some of their properties.

Existence, Uniqueness and Qualitative Properties of Global Solutions of Abstract Differential Equations with State-Dependent Delay

2019 ◽  
Vol 62 (3) ◽  
pp. 771-788 ◽  
Author(s):  
Eduardo Hernández ◽  
Jianhong Wu
Keyword(s):  
Population Dynamics ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Global Solutions ◽  
Almost Periodic ◽  
Qualitative Properties ◽  
Abstract Differential Equations ◽  
State Dependent ◽  
State Dependent Delay ◽  
Asymptotically Almost Periodic

AbstractWe study the existence, uniqueness and qualitative properties of global solutions of abstract differential equations with state-dependent delay. Results on the existence of almost periodic-type solutions (including, periodic, almost periodic, asymptotically almost periodic and almost automorphic solutions) are proved. Some examples of partial differential equations with state-dependent delay arising in population dynamics are presented.

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