Stepanov-like pseudo-almost automorphic solutions of infinite class in the alpha-norm under the light of measure theory
In this article, we study weighted Stepanov-like pseudo-almost automorphic functions with infinite delay using measure theory. We present a new concept of weighted ergodic functions, which is more general than the classical one. Then, we establish many interesting results on the space of such functi...
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| Format: | Article |
| Language: | English |
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De Gruyter
2024-11-01
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| Series: | Nonautonomous Dynamical Systems |
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| Online Access: | https://doi.org/10.1515/msds-2024-0003 |
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| author | Mbainadji Djendode Ngarmadji Kossadoum Koumla Sylvain |
| author_facet | Mbainadji Djendode Ngarmadji Kossadoum Koumla Sylvain |
| author_sort | Mbainadji Djendode |
| collection | DOAJ |
| description | In this article, we study weighted Stepanov-like pseudo-almost automorphic functions with infinite delay using measure theory. We present a new concept of weighted ergodic functions, which is more general than the classical one. Then, we establish many interesting results on the space of such functions. We also study the existence and uniqueness of (μ,ν)\left(\mu ,\nu )-Stepanov-like pseudo-almost automorphic solutions of infinite class in the α\alpha -norm for some partial functional differential equations in a Banach space with unbounded delay, using the spectral decomposition of the phase space developed by Adimy and his co-authors. An example is given to illustrate this work. |
| format | Article |
| id | doaj-art-5eb87b30b70a48eeb98d766dbeaf98d2 |
| institution | Kabale University |
| issn | 2353-0626 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Nonautonomous Dynamical Systems |
| spelling | doaj-art-5eb87b30b70a48eeb98d766dbeaf98d22024-11-25T11:18:24ZengDe GruyterNonautonomous Dynamical Systems2353-06262024-11-0111113410.1515/msds-2024-0003Stepanov-like pseudo-almost automorphic solutions of infinite class in the alpha-norm under the light of measure theoryMbainadji Djendode0Ngarmadji Kossadoum1Koumla Sylvain2Département de Mathématiques et Informatiques, Université Polytechnique de Mongo, B.P. 4377, Mongo, TchadDépartement de Mathématiques et Informatiques, École Normale Supérieure de Ndjaména, B.P. 206, Ndjaména, TchadDépartement de Mathématiques, Université Adam Barka, Faculté des Sciences et Techniques, B.P. 1117, Abéché, TchadIn this article, we study weighted Stepanov-like pseudo-almost automorphic functions with infinite delay using measure theory. We present a new concept of weighted ergodic functions, which is more general than the classical one. Then, we establish many interesting results on the space of such functions. We also study the existence and uniqueness of (μ,ν)\left(\mu ,\nu )-Stepanov-like pseudo-almost automorphic solutions of infinite class in the α\alpha -norm for some partial functional differential equations in a Banach space with unbounded delay, using the spectral decomposition of the phase space developed by Adimy and his co-authors. An example is given to illustrate this work.https://doi.org/10.1515/msds-2024-0003measure theoryergodicity(μ, ν)-seudo-almost automorphic functioninfinite delayevolution equationsreaction–diffusion systempartial functional differential equations34k1434k3035b1535k5744a3547d06 |
| spellingShingle | Mbainadji Djendode Ngarmadji Kossadoum Koumla Sylvain Stepanov-like pseudo-almost automorphic solutions of infinite class in the alpha-norm under the light of measure theory Nonautonomous Dynamical Systems measure theory ergodicity (μ, ν)-seudo-almost automorphic function infinite delay evolution equations reaction–diffusion system partial functional differential equations 34k14 34k30 35b15 35k57 44a35 47d06 |
| title | Stepanov-like pseudo-almost automorphic solutions of infinite class in the alpha-norm under the light of measure theory |
| title_full | Stepanov-like pseudo-almost automorphic solutions of infinite class in the alpha-norm under the light of measure theory |
| title_fullStr | Stepanov-like pseudo-almost automorphic solutions of infinite class in the alpha-norm under the light of measure theory |
| title_full_unstemmed | Stepanov-like pseudo-almost automorphic solutions of infinite class in the alpha-norm under the light of measure theory |
| title_short | Stepanov-like pseudo-almost automorphic solutions of infinite class in the alpha-norm under the light of measure theory |
| title_sort | stepanov like pseudo almost automorphic solutions of infinite class in the alpha norm under the light of measure theory |
| topic | measure theory ergodicity (μ, ν)-seudo-almost automorphic function infinite delay evolution equations reaction–diffusion system partial functional differential equations 34k14 34k30 35b15 35k57 44a35 47d06 |
| url | https://doi.org/10.1515/msds-2024-0003 |
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