Journal of Mathematical Analysis and Applications最新文献

{"title":"Symmetry results for the area formula in homogeneous groups","authors":"Francesca Corni ,&nbsp;Valentino Magnani","doi":"10.1016/j.jmaa.2025.129238","DOIUrl":"10.1016/j.jmaa.2025.129238","url":null,"abstract":"<div><div>We prove that if the shape of the metric unit ball in a homogeneous group enjoys a precise symmetry property, then the associated distance yields the standard form of the area formula. The result applies to some classes of smooth and nonsmooth submanifolds. We finally prove the equality between spherical measure and centered Hausdorff measure, under two different geometric conditions on the shape of the metric unit ball.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"546 2","pages":"Article 129238"},"PeriodicalIF":1.2,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143165971","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}

{"title":"Strict convexity of Orlicz spaces under renorming","authors":"Esra Başar ,&nbsp;Serap Öztop ,&nbsp;Badik Hüseyin Uysal ,&nbsp;Şeyma Yaşar","doi":"10.1016/j.jmaa.2025.129236","DOIUrl":"10.1016/j.jmaa.2025.129236","url":null,"abstract":"<div><div>Let Φ be an Orlicz function and <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>Φ</mi></mrow></msup><mo>(</mo><mi>X</mi><mo>,</mo><mi>Σ</mi><mo>,</mo><mi>μ</mi><mo>)</mo></math></span> be the corresponding Orlicz space on a non-atomic, <em>σ</em>-finite, complete measure space <span><math><mo>(</mo><mi>X</mi><mo>,</mo><mi>Σ</mi><mo>,</mo><mi>μ</mi><mo>)</mo></math></span>. It is known that strict convexity of the whole spaces are the most essential and important geometric notion in the geometric theory of Banach spaces. So, we describe the strict convexity of Orlicz spaces equipped with the <em>s</em>-norm and some of its consequences. On the other hand, it is known that the geometric properties of Orlicz space depends on the norm. Thus, our study generalizes and unifies the results that have been obtained for the Orlicz norm, the Luxemburg norm and the <em>p</em>-Amemiya norm separately.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"546 2","pages":"Article 129236"},"PeriodicalIF":1.2,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143165894","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}

{"title":"Multivariable pseudospectrum in C⁎-algebras","authors":"Alexander Cerjan ,&nbsp;Vasile Lauric ,&nbsp;Terry A. Loring","doi":"10.1016/j.jmaa.2025.129241","DOIUrl":"10.1016/j.jmaa.2025.129241","url":null,"abstract":"<div><div>We look at various forms of spectrum and associated pseudospectrum that can be defined for noncommuting <em>d</em>-tuples of Hermitian elements of a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebra. In particular, we focus on the forms of multivariable pseudospectra that are finding applications in physics. The emphasis is on theoretical calculations of examples, in particular for noncommuting pairs and triple of operators on infinite dimensional Hilbert space. In particular, we look at the universal pair of projections in a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebra, the usual position and momentum operators, and triples of tridiagonal operators. We prove a relation between the quadratic pseudospectrum and Clifford pseudospectra, as well as results about how symmetries in a tuple of operators can lead to a symmetry in the various pseudospectra.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"547 1","pages":"Article 129241"},"PeriodicalIF":1.2,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143166312","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}

{"title":"Self-regulation and resource dependent growth rates: A size-structured predator-prey model","authors":"Xuan Tian ,&nbsp;Shangjiang Guo ,&nbsp;Mimmo Iannelli ,&nbsp;Andrea Pugliese","doi":"10.1016/j.jmaa.2025.129231","DOIUrl":"10.1016/j.jmaa.2025.129231","url":null,"abstract":"<div><div>The dynamical behavior of a size-structured predator-prey model with nonlinear growth rates is studied. In the model prey growth rate decreases with prey population density, while predator growth rate depends on predation. Existence and uniqueness of solutions are proved under weak conditions. A threshold is established for the stability of the predator-free equilibrium and the existence of a positive equilibrium. When restricted only to the prey, the model is a special case of the one studied by Farkas and Hagen <span><span>[13]</span></span>; in this case it is shown that the positive equilibrium may undergo Hopf bifurcation, a novel feature in this class of models.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"546 2","pages":"Article 129231"},"PeriodicalIF":1.2,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143165782","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}

{"title":"New results on the global dynamics for a two-species chemotaxis system with two chemicals and logistic sources","authors":"Rabil Ayazoglu ,&nbsp;Ismail Ekincioglu","doi":"10.1016/j.jmaa.2025.129228","DOIUrl":"10.1016/j.jmaa.2025.129228","url":null,"abstract":"&lt;div&gt;&lt;div&gt;This paper deals with the following competitive two-species chemotaxis system with two chemicals with a source term of logistic type &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;χ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;υ&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;η&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;υ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mi&gt;υ&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;υ&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;χ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mo&gt;⋅&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;mi&gt;∇&lt;/mi&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;η&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;×&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; under homogeneous Neumann boundary conditions &lt;span&gt;&lt;math&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mo&gt;∂&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;∂&lt;/mo&gt;&lt;mi&gt;ν&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mo&gt;∂&lt;/mo&gt;&lt;mi&gt;υ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;∂&lt;/mo&gt;&lt;mi&gt;ν&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mo&gt;∂&lt;/mo&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;∂&lt;/mo&gt;&lt;mi&gt;ν&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mo&gt;∂&lt;/mo&gt;&lt;mi&gt;z&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;∂&lt;/mo&gt;&lt;mi&gt;ν&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mo&gt;∂&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;×&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; and initial conditions &lt;span&gt;&lt;math&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mi&gt;υ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;υ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;, in a bounded domain &lt;span&gt;&lt;math&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;⊂&lt;/mo&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;N&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, w","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"545 2","pages":"Article 129228"},"PeriodicalIF":1.2,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143148186","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}

{"title":"On the phenomenon of topological chaos and statistical triviality","authors":"Chao Liang ,&nbsp;Xiankun Ren ,&nbsp;Wenxiang Sun ,&nbsp;Edson Vargas","doi":"10.1016/j.jmaa.2025.129229","DOIUrl":"10.1016/j.jmaa.2025.129229","url":null,"abstract":"<div><div>There exists a compact manifold so that the set of topologically chaotic but statistically trivial <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>r</mi></mrow></msup><mo>(</mo><mn>1</mn><mo>≤</mo><mi>r</mi><mo>≤</mo><mo>∞</mo><mo>)</mo></math></span> vector fields on this manifold displays considerable scale in the view of dimension. More specifically, it contains an infinite-dimensional connected subset.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"546 2","pages":"Article 129229"},"PeriodicalIF":1.2,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143165783","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}

{"title":"Dirac operators on the half-line: Stability of spectrum and non-relativistic limit","authors":"David Kramár,&nbsp;David Krejčiřík","doi":"10.1016/j.jmaa.2025.129225","DOIUrl":"10.1016/j.jmaa.2025.129225","url":null,"abstract":"<div><div>We consider Dirac operators on the half-line, subject to generalised infinite-mass boundary conditions. We derive sufficient conditions which guarantee the stability of the spectrum against possibly non-self-adjoint potential perturbations and study the optimality of the obtained results. Finally, we establish a non-relativistic limit which makes a relationship of the present model to the Robin Laplacian on the half-line.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"546 2","pages":"Article 129225"},"PeriodicalIF":1.2,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143128050","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}

{"title":"Weighted fractional Hardy inequalities with singularity on any flat submanifold","authors":"Vivek Sahu","doi":"10.1016/j.jmaa.2025.129227","DOIUrl":"10.1016/j.jmaa.2025.129227","url":null,"abstract":"<div><div>We extend the work of Dyda and Kijaczko by establishing the corresponding weighted fractional Hardy inequalities with singularities on any flat submanifolds. While they derived weighted fractional Hardy inequalities with singularities at a point and on a half-space, we generalize these results to handle singularities on any flat submanifold of codimension <em>k</em>, where <span><math><mn>1</mn><mo>&lt;</mo><mi>k</mi><mo>&lt;</mo><mi>d</mi></math></span>. Furthermore, we also address the critical case <span><math><mi>s</mi><mi>p</mi><mo>=</mo><mi>k</mi><mo>+</mo><mi>α</mi><mo>+</mo><mi>β</mi></math></span> and establish weighted fractional Hardy inequality with appropriate logarithmic weight function.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"546 2","pages":"Article 129227"},"PeriodicalIF":1.2,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143165779","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}

{"title":"Boundedness criteria for a chemotaxis consumption model with gradient nonlinearities","authors":"Alessandro Columbu","doi":"10.1016/j.jmaa.2025.129226","DOIUrl":"10.1016/j.jmaa.2025.129226","url":null,"abstract":"<div><div>This work deals with the consumption chemotaxis problem<span><span><span><math><mrow><mo>{</mo><mtable><mtr><mtd><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mi>u</mi><mo>−</mo><mi>χ</mi><mi>∇</mi><mo>⋅</mo><mi>u</mi><mi>∇</mi><mi>v</mi><mo>+</mo><mi>λ</mi><mi>u</mi><mo>−</mo><mi>μ</mi><msup><mrow><mi>u</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><mi>c</mi><mo>|</mo><mi>∇</mi><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>γ</mi></mrow></msup><mo>,</mo></mtd><mtd><mtext>in</mtext><mspace></mspace><mi>Ω</mi><mo>×</mo><mo>(</mo><mn>0</mn><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mtext>max</mtext></mrow></msub><mo>)</mo><mo>,</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mi>v</mi><mo>−</mo><mi>u</mi><mi>v</mi><mo>,</mo></mtd><mtd><mtext>in</mtext><mspace></mspace><mi>Ω</mi><mo>×</mo><mo>(</mo><mn>0</mn><mo>,</mo><msub><mrow><mi>T</mi></mrow><mrow><mtext>max</mtext></mrow></msub><mo>)</mo><mo>,</mo></mtd></mtr></mtable></mrow></math></span></span></span> in a bounded and smooth domain <span><math><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>, <span><math><mi>n</mi><mo>≥</mo><mn>3</mn></math></span>, under homogeneous Neumann boundary conditions, for <span><math><mi>χ</mi><mo>,</mo><mi>λ</mi><mo>,</mo><mi>μ</mi><mo>,</mo><mi>c</mi><mo>&gt;</mo><mn>0</mn></math></span>, <span><math><msub><mrow><mi>T</mi></mrow><mrow><mtext>max</mtext></mrow></msub><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>]</mo></math></span> and for <span><math><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>v</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> positive initial data with a certain regularity. We will show that the problem has a unique and uniformly bounded classical solution for <span><math><mi>γ</mi><mo>∈</mo><mo>(</mo><mfrac><mrow><mn>2</mn><mi>n</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mfrac><mo>,</mo><mn>2</mn><mo>]</mo></math></span>. Moreover, we have the same result for <span><math><mi>γ</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mi>n</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></mfrac></math></span> and a condition that involves the parameters <span><math><mi>c</mi><mo>,</mo><mi>μ</mi><mo>,</mo><mi>n</mi><mo>,</mo><mi>χ</mi></math></span> and the initial data.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"546 1","pages":"Article 129226"},"PeriodicalIF":1.2,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143167399","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}

{"title":"Transitions of bifurcation diagrams of a forced heteroclinic cycle","authors":"Isabel S. Labouriau ,&nbsp;Alexandre A.P. Rodrigues","doi":"10.1016/j.jmaa.2025.129223","DOIUrl":"10.1016/j.jmaa.2025.129223","url":null,"abstract":"<div><div>A family of periodic perturbations of an attracting robust heteroclinic cycle defined on the two-sphere is studied by reducing the analysis to that of a one-parameter family of maps on a circle. The set of zeros of the family forms a bifurcation diagram on the cylinder. The different bifurcation diagrams and the transitions between them are obtained as the strength of attraction of the cycle and the amplitude of the periodic perturbation vary. We determine a threshold in the cycle's attraction strength above which frequency locked periodic solutions with arbitrarily long periods bifurcate from the cycle as the period of the perturbation decreases. Below this threshold further transitions are found giving rise to a frequency locked invariant torus and to a frequency locked suspended horseshoe, arising from heteroclinic tangencies in the family of maps.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"546 2","pages":"Article 129223"},"PeriodicalIF":1.2,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143165781","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}