Pub Date : 2023-09-29DOI: 10.1142/s0219530523500288
Claudianor O. Alves, Vincenzo Ambrosio
{"title":"Concentrating solutions for a fractional <i>p</i>-Laplacian logarithmic Schrodinger equation","authors":"Claudianor O. Alves, Vincenzo Ambrosio","doi":"10.1142/s0219530523500288","DOIUrl":"https://doi.org/10.1142/s0219530523500288","url":null,"abstract":"","PeriodicalId":55519,"journal":{"name":"Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135133292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-08DOI: 10.1142/s0219530523500252
Nuno Costa Dias, Joao Nuno Prata, Nenad Teofanov
{"title":"Gabor products and a phase space approach to nonlinear analysis","authors":"Nuno Costa Dias, Joao Nuno Prata, Nenad Teofanov","doi":"10.1142/s0219530523500252","DOIUrl":"https://doi.org/10.1142/s0219530523500252","url":null,"abstract":"","PeriodicalId":55519,"journal":{"name":"Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136362999","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-01DOI: 10.1142/s0219530523500203
M. L. Arenas-Blazquez, A. San Antolín
{"title":"Some compactly supported riesz wavelets associated to any Ed(2)(ℤ) Dilation","authors":"M. L. Arenas-Blazquez, A. San Antolín","doi":"10.1142/s0219530523500203","DOIUrl":"https://doi.org/10.1142/s0219530523500203","url":null,"abstract":"","PeriodicalId":55519,"journal":{"name":"Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44240846","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-01DOI: 10.1142/s0219530523500227
Yanyan Xu, Gaunggui Chen, Wenjing Lu
{"title":"Non-Linear Approximation of Functions by Sets of Finite Pseudo-dimension in the Probabilistic and Average Case Settings","authors":"Yanyan Xu, Gaunggui Chen, Wenjing Lu","doi":"10.1142/s0219530523500227","DOIUrl":"https://doi.org/10.1142/s0219530523500227","url":null,"abstract":"","PeriodicalId":55519,"journal":{"name":"Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46838468","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-01DOI: 10.1142/s0219530523500215
Vishvesh Kumar, Shyam Swarup Mondal
{"title":"Symbolic calculus and M-ellipticity of pseudo-differential operators on ℤn","authors":"Vishvesh Kumar, Shyam Swarup Mondal","doi":"10.1142/s0219530523500215","DOIUrl":"https://doi.org/10.1142/s0219530523500215","url":null,"abstract":"","PeriodicalId":55519,"journal":{"name":"Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41960130","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-18DOI: 10.1142/s0219530523500161
J. Cholewa, A. Rodríguez-Bernal
{"title":"On linear higher order parabolic equations in Morrey spaces","authors":"J. Cholewa, A. Rodríguez-Bernal","doi":"10.1142/s0219530523500161","DOIUrl":"https://doi.org/10.1142/s0219530523500161","url":null,"abstract":"","PeriodicalId":55519,"journal":{"name":"Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49101640","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-18DOI: 10.1142/s0219530523500185
A. Esfahani
{"title":"Prescribed solutions of a nonlinear fractional Schrodinger system with quadratic interaction","authors":"A. Esfahani","doi":"10.1142/s0219530523500185","DOIUrl":"https://doi.org/10.1142/s0219530523500185","url":null,"abstract":"","PeriodicalId":55519,"journal":{"name":"Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44225541","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-18DOI: 10.1142/s0219530523500173
A. Gruber, Á. Pámpano, M. Toda
{"title":"Instability of Closed p-Elastic Curves in 𝕊2","authors":"A. Gruber, Á. Pámpano, M. Toda","doi":"10.1142/s0219530523500173","DOIUrl":"https://doi.org/10.1142/s0219530523500173","url":null,"abstract":"","PeriodicalId":55519,"journal":{"name":"Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46536233","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-05DOI: 10.1142/s0219530523500112
H. Mohebalizadeh, G. Fasshauer, H. Adibi
This paper extends the work of Fasshauer and Ye [Reproducing kernels of Sobolev spaces via a Green kernel approach with differential operators and boundary operators, Adv. Comput. Math. 38(4) (2011) 891921] in two different ways, namely, new kernels and associated native spaces are identified as crucial Hilbert spaces in applied mathematics. These spaces include the following spaces defined in bounded domains [Formula: see text] with smooth boundary: homogeneous Sobolev–Slobodeckij̆ spaces, denoted by [Formula: see text], and Sobolev–Slobodeckij̆ spaces, denoted by [Formula: see text], where [Formula: see text]. Our goal is accomplished by obtaining the Green’s solutions of equations involving the fractional Laplacian and fractional differential operators defined through interpolation theory. We provide a proof that the Green’s kernels satisfying these problems are symmetric and positive definite reproducing kernels of [Formula: see text] and [Formula: see text], respectively. Constructing kernels in these two ways enables the characterization of functions in native spaces based on their regularity. The Galerkin/collocation method, based on these kernels, is employed to solve various fractional problems, offering explicit or simplified calculations and efficient solutions. This method yields improved results with reduced computational costs, making it suitable for complex domains.
{"title":"Reproducing kernels of Sobolev–Slobodeckij̆ spaces via Green’s kernel approach: Theory and applications","authors":"H. Mohebalizadeh, G. Fasshauer, H. Adibi","doi":"10.1142/s0219530523500112","DOIUrl":"https://doi.org/10.1142/s0219530523500112","url":null,"abstract":"This paper extends the work of Fasshauer and Ye [Reproducing kernels of Sobolev spaces via a Green kernel approach with differential operators and boundary operators, Adv. Comput. Math. 38(4) (2011) 891921] in two different ways, namely, new kernels and associated native spaces are identified as crucial Hilbert spaces in applied mathematics. These spaces include the following spaces defined in bounded domains [Formula: see text] with smooth boundary: homogeneous Sobolev–Slobodeckij̆ spaces, denoted by [Formula: see text], and Sobolev–Slobodeckij̆ spaces, denoted by [Formula: see text], where [Formula: see text]. Our goal is accomplished by obtaining the Green’s solutions of equations involving the fractional Laplacian and fractional differential operators defined through interpolation theory. We provide a proof that the Green’s kernels satisfying these problems are symmetric and positive definite reproducing kernels of [Formula: see text] and [Formula: see text], respectively. Constructing kernels in these two ways enables the characterization of functions in native spaces based on their regularity. The Galerkin/collocation method, based on these kernels, is employed to solve various fractional problems, offering explicit or simplified calculations and efficient solutions. This method yields improved results with reduced computational costs, making it suitable for complex domains.","PeriodicalId":55519,"journal":{"name":"Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47307360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-04DOI: 10.1142/s0219530523500124
M. Jleli, B. Samet
We consider a system of nonlinear biharmonic wave inequalities posed in an exterior domain of [Formula: see text]. Three types of boundary conditions are investigated. For each case, the existence and nonexistence of weak solutions are studied. Our study yields naturally existence and nonexistence results for the corresponding stationary system and equation. Many new results are provided and some open questions are proposed.
{"title":"Existence and nonexistence criteria for a system of biharmonic wave inequalities in an exterior domain of ℝN","authors":"M. Jleli, B. Samet","doi":"10.1142/s0219530523500124","DOIUrl":"https://doi.org/10.1142/s0219530523500124","url":null,"abstract":"We consider a system of nonlinear biharmonic wave inequalities posed in an exterior domain of [Formula: see text]. Three types of boundary conditions are investigated. For each case, the existence and nonexistence of weak solutions are studied. Our study yields naturally existence and nonexistence results for the corresponding stationary system and equation. Many new results are provided and some open questions are proposed.","PeriodicalId":55519,"journal":{"name":"Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42419768","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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