Pub Date : 2022-12-23DOI: 10.31392/mfat-npu26_1.2021.07
L. Moutaouekkil, O. Chakrone, Z. El Allali, S. Taarabti
In this article, we consider the following high-order p-Laplacian neutral differential equation with multiple deviating arguments:$$(varphi_{p}(x(t)-cx(t-r))^{(m)}(t)))^{(m)}= f(x(t))x'(t)+g(t,x(t),x(t-tau_{1}(t)),...,x(t-tau_{k}(t)))+e(t).$$By appling the continuation theorem, theory of Fourier series, Bernoulli numbers theory and some analytic techniques, sufficient conditions for the existence of periodic solutions are established.
{"title":"New results on the existence of periodic solutions for a higher-order p -Laplacian neutral differential equation with multiple deviating arguments","authors":"L. Moutaouekkil, O. Chakrone, Z. El Allali, S. Taarabti","doi":"10.31392/mfat-npu26_1.2021.07","DOIUrl":"https://doi.org/10.31392/mfat-npu26_1.2021.07","url":null,"abstract":"In this article, we consider the following high-order p-Laplacian neutral differential equation with multiple deviating arguments:$$(varphi_{p}(x(t)-cx(t-r))^{(m)}(t)))^{(m)}= f(x(t))x'(t)+g(t,x(t),x(t-tau_{1}(t)),...,x(t-tau_{k}(t)))+e(t).$$By appling the continuation theorem, theory of Fourier series, Bernoulli numbers theory and some analytic techniques, sufficient conditions for the existence of periodic solutions are established.","PeriodicalId":44325,"journal":{"name":"Methods of Functional Analysis and Topology","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46688176","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-28DOI: 10.31392/mfat-npu26_2.2021.06
D. Finkelshtein, Y. Kondratiev, Peter Kuchling
Configuration spaces form an important and actively developing area in the infinite dimensional analysis. The spaces not only contain rich mathematical structures which require non-trivial combination of continuous and combinatoric analysis, they also provide a natural mathematical framework for the applications to mathematical physics, biology, ecology, and beyond. Spaces of discrete Radon measures (DRM) may be considered as generalizations of configuration spaces. Main peculiarity of a DRM is that its support is typically not a configuration (i.e. not a locally finite set). The latter changes drastically the techniques for the study of the spaces of DRM. Spaces of DRM have various motivations coming from mathematics and applications. In particular, random DRM appear in the context of the Skorokhod theorem [17] in the theory of processes with independent increments. Next, in the representation theory of current groups, the role of measures on spaces of DRM was clarified in fundamental works by Gelfand, Graev, and Vershik; see [15] for the development of this approach. Additionally, DRM gives a useful technical equipment in the study of several models in mathematical physics, biology, and ecology. In the present paper, we start with a brief overview of the known facts about the spaces of DRM (Section 2). In [10], the concept of Plato subspaces of the spaces of marked configurations was introduced. Using this, one can define topological, differential and functional structures on spaces of DRM, as well as transfer the harmonic analysis considered in [11] to the spaces of DRM. This allows us to extend the study of nonequilibrium dynamics, see e.g. [8, 12, 13], to the spaces of DRM.
{"title":"Markov dynamics on the cone of discrete Radon measures","authors":"D. Finkelshtein, Y. Kondratiev, Peter Kuchling","doi":"10.31392/mfat-npu26_2.2021.06","DOIUrl":"https://doi.org/10.31392/mfat-npu26_2.2021.06","url":null,"abstract":"Configuration spaces form an important and actively developing area in the infinite dimensional analysis. The spaces not only contain rich mathematical structures which require non-trivial combination of continuous and combinatoric analysis, they also provide a natural mathematical framework for the applications to mathematical physics, biology, ecology, and beyond. Spaces of discrete Radon measures (DRM) may be considered as generalizations of configuration spaces. Main peculiarity of a DRM is that its support is typically not a configuration (i.e. not a locally finite set). The latter changes drastically the techniques for the study of the spaces of DRM. Spaces of DRM have various motivations coming from mathematics and applications. In particular, random DRM appear in the context of the Skorokhod theorem [17] in the theory of processes with independent increments. Next, in the representation theory of current groups, the role of measures on spaces of DRM was clarified in fundamental works by Gelfand, Graev, and Vershik; see [15] for the development of this approach. Additionally, DRM gives a useful technical equipment in the study of several models in mathematical physics, biology, and ecology. In the present paper, we start with a brief overview of the known facts about the spaces of DRM (Section 2). In [10], the concept of Plato subspaces of the spaces of marked configurations was introduced. Using this, one can define topological, differential and functional structures on spaces of DRM, as well as transfer the harmonic analysis considered in [11] to the spaces of DRM. This allows us to extend the study of nonequilibrium dynamics, see e.g. [8, 12, 13], to the spaces of DRM.","PeriodicalId":44325,"journal":{"name":"Methods of Functional Analysis and Topology","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44509714","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.31392/mfat-npu26_1.2021.08
I. Özdemir
{"title":"Asymptotically stable solutions of a nonlinear integral equation","authors":"I. Özdemir","doi":"10.31392/mfat-npu26_1.2021.08","DOIUrl":"https://doi.org/10.31392/mfat-npu26_1.2021.08","url":null,"abstract":"","PeriodicalId":44325,"journal":{"name":"Methods of Functional Analysis and Topology","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69691723","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.31392/mfat-npu26_3.2021.03
O. Boyko, O. Martynyuk, V. Pivovarchik
The largest possible multiplicity of an eigenvalue of a spectral problem generated by the Stieltjes string equations on a metric tree is ppen 1, where ppen is the number of pendant vertices. We propose how to find the second largest possible multiplicity of an eigenvalue of such a problem. This multiplicity depends on the numbers of point masses on the edges of the trees. Максимально можлива кратнiсть власного значення спектральної задачi, породженої рiвняннями струни Стiлтьєса на метричному деревi, дорiвнює ppen 1, де ppen — кiлькiсть висячих вершин. Ми пропонуємо, як знайти другу за величиною кратнiсть власного значення такої задачi. Ця кратнiсть залежить вiд кiлькостi точкових мас на ребрах дерев.
{"title":"On the second largest multiplicity of eigenvalues for the Stieltjes string spectral problem on trees","authors":"O. Boyko, O. Martynyuk, V. Pivovarchik","doi":"10.31392/mfat-npu26_3.2021.03","DOIUrl":"https://doi.org/10.31392/mfat-npu26_3.2021.03","url":null,"abstract":"The largest possible multiplicity of an eigenvalue of a spectral problem generated by the Stieltjes string equations on a metric tree is ppen 1, where ppen is the number of pendant vertices. We propose how to find the second largest possible multiplicity of an eigenvalue of such a problem. This multiplicity depends on the numbers of point masses on the edges of the trees. Максимально можлива кратнiсть власного значення спектральної задачi, породженої рiвняннями струни Стiлтьєса на метричному деревi, дорiвнює ppen 1, де ppen — кiлькiсть висячих вершин. Ми пропонуємо, як знайти другу за величиною кратнiсть власного значення такої задачi. Ця кратнiсть залежить вiд кiлькостi точкових мас на ребрах дерев.","PeriodicalId":44325,"journal":{"name":"Methods of Functional Analysis and Topology","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69692340","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.31392/mfat-npu26_4.2021.11
Rakia Ahmed Yahia, A. Benchaabane, Halim zeghdoudi
{"title":"Existence results for second-order neutral stochastic equations driven by Rosenblatt process","authors":"Rakia Ahmed Yahia, A. Benchaabane, Halim zeghdoudi","doi":"10.31392/mfat-npu26_4.2021.11","DOIUrl":"https://doi.org/10.31392/mfat-npu26_4.2021.11","url":null,"abstract":"","PeriodicalId":44325,"journal":{"name":"Methods of Functional Analysis and Topology","volume":"11 2 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69692392","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.31392/mfat-npu26_4.2021.07
M. Gil'
{"title":"On Location of the Spectrum of an Operator with a Hilbert-Schmidt Resolvent in the Left Half-Plane","authors":"M. Gil'","doi":"10.31392/mfat-npu26_4.2021.07","DOIUrl":"https://doi.org/10.31392/mfat-npu26_4.2021.07","url":null,"abstract":"","PeriodicalId":44325,"journal":{"name":"Methods of Functional Analysis and Topology","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69692703","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.31392/mfat-npu26_4.2021.03
W. Bock, Ang Elyn Gumanoy
{"title":"Generalized Mittag-Leffler Kernels and Generalized Scaling Operators in Mittag-Leffler Analysis","authors":"W. Bock, Ang Elyn Gumanoy","doi":"10.31392/mfat-npu26_4.2021.03","DOIUrl":"https://doi.org/10.31392/mfat-npu26_4.2021.03","url":null,"abstract":"","PeriodicalId":44325,"journal":{"name":"Methods of Functional Analysis and Topology","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69692134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.31392/mfat-npu26_2.2021.04
Y. Bouhafsi, M. Ech-chad, M. Missouri
{"title":"A Remark on the Range Closures of an Elementary Operator","authors":"Y. Bouhafsi, M. Ech-chad, M. Missouri","doi":"10.31392/mfat-npu26_2.2021.04","DOIUrl":"https://doi.org/10.31392/mfat-npu26_2.2021.04","url":null,"abstract":"","PeriodicalId":44325,"journal":{"name":"Methods of Functional Analysis and Topology","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69691868","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.31392/mfat-npu26_4.2021.02
Bhuwan Prasad Ojha, P. M. Bajracharya
{"title":"Some remarks on the generalization of orthogonality in terms of operators","authors":"Bhuwan Prasad Ojha, P. M. Bajracharya","doi":"10.31392/mfat-npu26_4.2021.02","DOIUrl":"https://doi.org/10.31392/mfat-npu26_4.2021.02","url":null,"abstract":"","PeriodicalId":44325,"journal":{"name":"Methods of Functional Analysis and Topology","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69692118","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.31392/mfat-npu26_1.2021.10
M. Rashid
{"title":"Tensor product and variants of Weyl's type theorem for p - w -hyponormal operators","authors":"M. Rashid","doi":"10.31392/mfat-npu26_1.2021.10","DOIUrl":"https://doi.org/10.31392/mfat-npu26_1.2021.10","url":null,"abstract":"","PeriodicalId":44325,"journal":{"name":"Methods of Functional Analysis and Topology","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69691416","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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