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On solutions of a semilinear measure-driven evolution equation with nonlocal conditions on infinite interval 论无限区间上带有非局部条件的半线性度量驱动演化方程的解
IF 0.8 3区 数学
Mathematische Nachrichten Pub Date : 2024-04-26 DOI: 10.1002/mana.202300243
Jiankun Wu, Xianlong Fu
{"title":"On solutions of a semilinear measure-driven evolution equation with nonlocal conditions on infinite interval","authors":"Jiankun Wu,&nbsp;Xianlong Fu","doi":"10.1002/mana.202300243","DOIUrl":"10.1002/mana.202300243","url":null,"abstract":"<p>This paper studies the existence and asymptotic properties of solutions for a semilinear measure-driven evolution equation with nonlocal conditions on an infinite interval. The existence result of the solutions for the considered equation is established by Schauder's fixed point theorem. Then, the asymptotic stability of solutions is further proved to show that all the solutions may converge to the unique solution of the corresponding Cauchy problem. In addition, under some conditions the existence of global attracting sets and quasi-invariant sets of mild solutions is investigated as well. Finally, an example is provided to illustrate the applications of the obtained results.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140809613","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Criticality of general two-term even-order linear difference equation via a chain of recessive solutions 通过隐性解链实现一般二项偶阶线性差分方程的临界性
IF 0.8 3区 数学
Mathematische Nachrichten Pub Date : 2024-04-26 DOI: 10.1002/mana.202300090
Jan Jekl
{"title":"Criticality of general two-term even-order linear difference equation via a chain of recessive solutions","authors":"Jan Jekl","doi":"10.1002/mana.202300090","DOIUrl":"10.1002/mana.202300090","url":null,"abstract":"<p>In this paper, the author investigates particular disconjugate even-order linear difference equations with two terms and classify them based on the properties of their recessive solutions at plus and minus infinity. The main theorem described states that the studied equation is <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>k</mi>\u0000 <mo>−</mo>\u0000 <mi>p</mi>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(k-p+1)$</annotation>\u0000 </semantics></math>-critical whenever a specific second-order linear difference equation is <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-critical. In the proof, the author derived closed-form solutions for the studied equation wherein the solutions of the said second-order equation appear. Furthermore, the solutions were organized, in order to determine recessive solutions, into a linear chain by sequence ordering that compares the solutions at <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>±</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <annotation>$pm infty$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140813012","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Two-weight extrapolation on function spaces and applications 函数空间上的二重外推法及其应用
IF 0.8 3区 数学
Mathematische Nachrichten Pub Date : 2024-04-22 DOI: 10.1002/mana.202300120
Mingming Cao, Andrea Olivo
{"title":"Two-weight extrapolation on function spaces and applications","authors":"Mingming Cao,&nbsp;Andrea Olivo","doi":"10.1002/mana.202300120","DOIUrl":"10.1002/mana.202300120","url":null,"abstract":"<p>This paper is devoted to studying the extrapolation theory of Rubio de Francia on general function spaces. We present endpoint extrapolation results including <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>A</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <annotation>$A_1$</annotation>\u0000 </semantics></math>, <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>A</mi>\u0000 <mi>p</mi>\u0000 </msub>\u0000 <annotation>$A_p$</annotation>\u0000 </semantics></math>, and <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>A</mi>\u0000 <mi>∞</mi>\u0000 </msub>\u0000 <annotation>$A_infty$</annotation>\u0000 </semantics></math> extrapolation in the context of Banach function spaces, and also on modular spaces. We also include several applications that can be easily obtained using extrapolation: local decay estimates for various operators, Coifman–Fefferman inequalities that can be used to show some known sharp <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>A</mi>\u0000 <mn>1</mn>\u0000 </msub>\u0000 <annotation>$A_1$</annotation>\u0000 </semantics></math> inequalities, Muckenhoupt–Wheeden and Sawyer's conjectures are also presented for many operators, which go beyond Calderón–Zygmund operators. Finally, we obtain two-weight inequalities for Littlewood–Paley operators and Fourier integral operators on weighted Banach function spaces.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140672753","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Asymptotics for a parabolic problem of Kirchhoff type with singular critical exponential nonlinearity 具有奇异临界指数非线性的基尔霍夫型抛物线问题的渐近论
IF 0.8 3区 数学
Mathematische Nachrichten Pub Date : 2024-04-21 DOI: 10.1002/mana.202200319
Tahir Boudjeriou
{"title":"Asymptotics for a parabolic problem of Kirchhoff type with singular critical exponential nonlinearity","authors":"Tahir Boudjeriou","doi":"10.1002/mana.202200319","DOIUrl":"10.1002/mana.202200319","url":null,"abstract":"<p>The main objective of this paper is to characterize stable sets based on the asymptotic behavior of solutions as <span></span><math>\u0000 <semantics>\u0000 <mi>t</mi>\u0000 <annotation>$t$</annotation>\u0000 </semantics></math> goes to infinity for the following class of parabolic Kirchhoff equations:\u0000\u0000 </p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140678379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On varieties whose general surface section has negative Kodaira dimension 关于一般表面截面具有负科代拉维度的品种
IF 0.8 3区 数学
Mathematische Nachrichten Pub Date : 2024-04-19 DOI: 10.1002/mana.202300565
Ciro Ciliberto, Claudio Fontanari
{"title":"On varieties whose general surface section has negative Kodaira dimension","authors":"Ciro Ciliberto,&nbsp;Claudio Fontanari","doi":"10.1002/mana.202300565","DOIUrl":"10.1002/mana.202300565","url":null,"abstract":"<p>In this paper, inspired by work of Fano, Morin, and Campana–Flenner, we give a projective classification of varieties of dimension 3 whose general hyperplane sections have negative Kodaira dimension, and we partly extend such a classification to varieties of dimension <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>⩾</mo>\u0000 <mn>4</mn>\u0000 </mrow>\u0000 <annotation>$ngeqslant 4$</annotation>\u0000 </semantics></math> whose general surface sections have negative Kodaira dimension. In particular, we prove that a variety of dimension <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>⩾</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <annotation>$ngeqslant 3$</annotation>\u0000 </semantics></math> whose general surface sections have negative Kodaira dimension is birationally equivalent to the product of a general surface section times <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>P</mi>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>−</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 <annotation>${mathbb {P}}^{n-2}$</annotation>\u0000 </semantics></math> unless (possibly) if the variety is a cubic hypersurface.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140630196","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Erratum to “A footnote to a theorem of Kawamata” 对 "川俣定理的脚注 "的勘误
IF 1 3区 数学
Mathematische Nachrichten Pub Date : 2024-04-19 DOI: 10.1002/mana.202400019
Osamu Fujino, Margarida Mendes Lopes, Rita Pardini, Sofia Tirabassi
{"title":"Erratum to “A footnote to a theorem of Kawamata”","authors":"Osamu Fujino, Margarida Mendes Lopes, Rita Pardini, Sofia Tirabassi","doi":"10.1002/mana.202400019","DOIUrl":"https://doi.org/10.1002/mana.202400019","url":null,"abstract":"We give an alternative proof of Theorem A in the paper: Mendes Lopes, Pardini, Tirabassi, A footnote to a theorem of Kawamata. We also explain how to fill a gap in the original proof.","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140630070","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Analytic Nullstellensätze and the model theory of valued fields 解析零点定理与有价域模型理论
IF 0.8 3区 数学
Mathematische Nachrichten Pub Date : 2024-04-14 DOI: 10.1002/mana.202200280
Matthias Aschenbrenner, Ahmed Srhir
{"title":"Analytic Nullstellensätze and the model theory of valued fields","authors":"Matthias Aschenbrenner,&nbsp;Ahmed Srhir","doi":"10.1002/mana.202200280","DOIUrl":"10.1002/mana.202200280","url":null,"abstract":"<p>We present a uniform framework for establishing Nullstellensätze for power series rings using quantifier elimination results for valued fields. As an application, we obtain Nullstellensätze for <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-adic power series (both formal and convergent) analogous to Rückert's complex and Risler's real Nullstellensatz, as well as a <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-adic analytic version of Hilbert's 17th Problem. Analogous statements for restricted power series, both real and <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-adic, are also considered.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.202200280","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140569493","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Groups having minimal covering number 2 of the diagonal type 最小覆盖数为 2 的对角线类型群
IF 0.8 3区 数学
Mathematische Nachrichten Pub Date : 2024-04-14 DOI: 10.1002/mana.202400096
Marco Fusari, Andrea Previtali, Pablo Spiga
{"title":"Groups having minimal covering number 2 of the diagonal type","authors":"Marco Fusari,&nbsp;Andrea Previtali,&nbsp;Pablo Spiga","doi":"10.1002/mana.202400096","DOIUrl":"10.1002/mana.202400096","url":null,"abstract":"<p>Garonzi and Lucchini explored finite groups <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> possessing a normal 2-covering, where no proper quotient of <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> exhibits such a covering. Their investigation offered a comprehensive overview of these groups, delineating that such groups fall into distinct categories: almost simple, affine, product action, or diagonal.</p><p>In this paper, we focus on the family falling under the diagonal type. Specifically, we present a thorough classification of finite diagonal groups possessing a normal 2-covering, with the attribute that no proper quotient of <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> has such a covering.</p><p>With deep appreciation to Martino Garonzi and Andrea Lucchini, for keeping us entertained.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140569383","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Nonsymmetric Lévy-type operators 非对称莱维型算子
IF 1 3区 数学
Mathematische Nachrichten Pub Date : 2024-04-11 DOI: 10.1002/mana.202300150
Jakub Minecki, Karol Szczypkowski
{"title":"Nonsymmetric Lévy-type operators","authors":"Jakub Minecki,&nbsp;Karol Szczypkowski","doi":"10.1002/mana.202300150","DOIUrl":"10.1002/mana.202300150","url":null,"abstract":"<p>We present a general approach to the parametrix construction. We apply it to prove the uniqueness and existence of a weak fundamental solution for the equation <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>∂</mi>\u0000 <mi>t</mi>\u0000 </msub>\u0000 <mi>u</mi>\u0000 <mo>=</mo>\u0000 <mi>L</mi>\u0000 <mi>u</mi>\u0000 </mrow>\u0000 <annotation>$partial _t u ={mathcal {L}}u$</annotation>\u0000 </semantics></math> with nonsymmetric nonlocal operators\u0000\u0000 </p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140569382","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Geometric and analytic results for Einstein solitons 爱因斯坦孤子的几何和解析结果
IF 0.8 3区 数学
Mathematische Nachrichten Pub Date : 2024-04-10 DOI: 10.1002/mana.202200340
Enrique F. L. Agila, José N. V. Gomes
{"title":"Geometric and analytic results for Einstein solitons","authors":"Enrique F. L. Agila,&nbsp;José N. V. Gomes","doi":"10.1002/mana.202200340","DOIUrl":"10.1002/mana.202200340","url":null,"abstract":"<p>We compute a lower bound for the scalar curvature of a gradient Einstein soliton under a certain assumption on its potential function. We establish an asymptotic behavior of the potential function on a noncompact gradient shrinking Einstein soliton. As a result, we obtain the finiteness of its fundamental group and its weighted volume. We also prove some geometric and analytic results for constructing gradient Einstein solitons that are realized as warped metrics, and we give a few explicit examples.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140569387","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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