Journal of Mathematical Analysis and Applications最新文献

{"title":"On the planar weakly coupled nonlinear logarithmic Choquard systems","authors":"J.C. de Albuquerque ,&nbsp;J. Carvalho ,&nbsp;E. Medeiros","doi":"10.1016/j.jmaa.2025.129501","DOIUrl":"10.1016/j.jmaa.2025.129501","url":null,"abstract":"<div><div>In this paper, we study the following class of coupled nonlinear logarithmic Choquard equations<span><span><span><math><mrow><mo>{</mo><mtable><mtr><mtd><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>+</mo><msub><mrow><mi>λ</mi></mrow><mrow><mn>1</mn></mrow></msub><mi>u</mi></mtd><mtd><mo>=</mo><mrow><mo>(</mo><mi>log</mi><mo>⁡</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mo>|</mo><mo>⋅</mo><mo>|</mo></mrow></mfrac><mo>⁎</mo><msup><mrow><mi>u</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mi>u</mi><mo>+</mo><mrow><mo>(</mo><mi>log</mi><mo>⁡</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mo>|</mo><mo>⋅</mo><mo>|</mo></mrow></mfrac><mo>⁎</mo><msup><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mi>u</mi><mo>,</mo></mtd><mtd><mspace></mspace><mtext>in </mtext><mspace></mspace><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>,</mo></mtd></mtr><mtr><mtd><mo>−</mo><mi>Δ</mi><mi>v</mi><mo>+</mo><msub><mrow><mi>λ</mi></mrow><mrow><mn>2</mn></mrow></msub><mi>v</mi></mtd><mtd><mo>=</mo><mrow><mo>(</mo><mi>log</mi><mo>⁡</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mo>|</mo><mo>⋅</mo><mo>|</mo></mrow></mfrac><mo>⁎</mo><msup><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mi>v</mi><mo>+</mo><mrow><mo>(</mo><mi>log</mi><mo>⁡</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mo>|</mo><mo>⋅</mo><mo>|</mo></mrow></mfrac><mo>⁎</mo><msup><mrow><mi>u</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow><mi>v</mi><mo>,</mo></mtd><mtd><mspace></mspace><mtext>in </mtext><mspace></mspace><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>.</mo></mtd></mtr></mtable></mrow></math></span></span></span> We prove the existence of a nonnegative vector solution when <span><math><msub><mrow><mi>λ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><msub><mrow><mi>λ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>. Moreover, we prove that if <span><math><msub><mrow><mi>λ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>≠</mo><msub><mrow><mi>λ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>, then the system admits only the semi-trivial solution. Our approach is based on minimization over Nehari manifold and a version of the Principle of Symmetric Criticality due to Palais.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 1","pages":"Article 129501"},"PeriodicalIF":1.2,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143679331","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":"Transport multi-paths with capacity constraints","authors":"Qinglan Xia ,&nbsp;Haotian Sun","doi":"10.1016/j.jmaa.2025.129499","DOIUrl":"10.1016/j.jmaa.2025.129499","url":null,"abstract":"<div><div>This article generalizes the study of branched/ramified optimal transportation to those with capacity constraints. Each admissible transport network studied here is represented by a transport multi-path between measures, with a capacity constraint on each of its components. The associated transport cost is given by the sum of the <span><math><msub><mrow><mtext>M</mtext></mrow><mrow><mi>α</mi></mrow></msub></math></span>-cost of each component. Using this new formulation, we prove the existence of an optimal solution and provide an upper bound on the number of components for the solution. Additionally, we conduct analytical examinations of the properties (e.g. “map-compatibility”, and “simple common-source property”) of each solution component and explore the interplay among components, particularly in the discrete case.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 1","pages":"Article 129499"},"PeriodicalIF":1.2,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143679332","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":"On fractional p(⋅)-Schrödinger-Kirchhoff equations with the critical exponent in RN","authors":"Shuai Li ,&nbsp;Tianqing An ,&nbsp;Weichun Bu","doi":"10.1016/j.jmaa.2025.129502","DOIUrl":"10.1016/j.jmaa.2025.129502","url":null,"abstract":"<div><div>In the present paper, we discuss a class of critical Schrödinger-Kirchhoff type problem involving the fractional <span><math><mi>p</mi><mo>(</mo><mo>⋅</mo><mo>)</mo></math></span>-Laplacian. Firstly, for the critical case, we analyze the loss of compactness of the problem using the famous concentration-compactness principles. Next, the existence of nontrivial solutions is derived by utilizing the Nehari manifold approach. Finally, a simple example is given to show the validity of our main theorem's conditions. Our study improves and extends some recent work in the literature.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 1","pages":"Article 129502"},"PeriodicalIF":1.2,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143705543","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":"Bicomplex generalized hypergeometric functions and their applications","authors":"Snehasis Bera ,&nbsp;Sourav Das ,&nbsp;Abhijit Banerjee","doi":"10.1016/j.jmaa.2025.129490","DOIUrl":"10.1016/j.jmaa.2025.129490","url":null,"abstract":"<div><div>In this work, generalized hypergeometric functions for a bicomplex argument are introduced and the convergence criteria are derived. Furthermore, an integral representation of these functions is established. Moreover, quadratic transformation, a differential relation, analyticity, and contiguous relations of these functions are derived. Additionally, applications in quantum information systems and quantum optics are provided as a consequence.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 1","pages":"Article 129490"},"PeriodicalIF":1.2,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143715541","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":"Two-dimensional Schrödinger operators with non-local singular potentials","authors":"Lukáš Heriban ,&nbsp;Markus Holzmann ,&nbsp;Christian Stelzer-Landauer ,&nbsp;Georg Stenzel ,&nbsp;Matěj Tušek","doi":"10.1016/j.jmaa.2025.129498","DOIUrl":"10.1016/j.jmaa.2025.129498","url":null,"abstract":"<div><div>In this paper we introduce and study a family of self-adjoint realizations of the Laplacian in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> with a new type of transmission conditions along a closed bi-Lipschitz curve Σ. These conditions incorporate jumps in the Dirichlet traces both of the functions in the operator domains and of their Wirtinger derivatives and are non-local. Constructing a convenient generalized boundary triple, they may be parametrized by all compact self-adjoint operators in <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><mi>Σ</mi><mo>;</mo><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span>. Whereas for all choices of parameters the essential spectrum is stable and equal to <span><math><mo>[</mo><mn>0</mn><mo>,</mo><mo>+</mo><mo>∞</mo><mo>)</mo></math></span>, the discrete spectrum exhibits diverse behavior. While in many cases it is finite, we will describe also a class of parameters for which the discrete spectrum is infinite and accumulates at −∞. The latter class contains a non-local version of the oblique transmission conditions. Finally, we will connect the current model to its relativistic counterpart studied recently in <span><span>[33]</span></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 2","pages":"Article 129498"},"PeriodicalIF":1.2,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143704572","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":"The elliptic functions of Dixon and Du Val","authors":"P.L. Robinson","doi":"10.1016/j.jmaa.2025.129496","DOIUrl":"10.1016/j.jmaa.2025.129496","url":null,"abstract":"<div><div>We demonstrate and elaborate upon the very intimate relationship between the elliptic functions sm and cm of Dixon and the ternary elliptic functions of Du Val.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 1","pages":"Article 129496"},"PeriodicalIF":1.2,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143704789","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":"An extension of Petek-Šemrl preserver theorems for Jordan embeddings of structural matrix algebras","authors":"Ilja Gogić,&nbsp;Mateo Tomašević","doi":"10.1016/j.jmaa.2025.129497","DOIUrl":"10.1016/j.jmaa.2025.129497","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Let &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; be the algebra of &lt;span&gt;&lt;math&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;×&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; complex matrices and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;⊆&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; the corresponding upper-triangular subalgebra. In their influential work, Petek and Šemrl characterize Jordan automorphisms of &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;, when &lt;span&gt;&lt;math&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;, as (injective in the case of &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;) continuous commutativity and spectrum preserving maps &lt;span&gt;&lt;math&gt;&lt;mi&gt;ϕ&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mi&gt;ϕ&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;. Recently, in a joint work with Petek, the authors extended this characterization to the maps &lt;span&gt;&lt;math&gt;&lt;mi&gt;ϕ&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;, where &lt;span&gt;&lt;math&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; is an arbitrary subalgebra of &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; that contains &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;. In particular, any such map &lt;em&gt;ϕ&lt;/em&gt; is a Jordan embedding and hence of the form &lt;span&gt;&lt;math&gt;&lt;mi&gt;ϕ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; or &lt;span&gt;&lt;math&gt;&lt;mi&gt;ϕ&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt;, for some invertible matrix &lt;span&gt;&lt;math&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;.&lt;/div&gt;&lt;div&gt;In this paper we further extend the aforementioned results in the context of structural matrix algebras (SMAs), i.e. subalgebras &lt;span&gt;&lt;math&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; of &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; that contain all diagonal matrices. More precisely, we provide both a necessary and sufficient condition for an SMA &lt;span&gt;&lt;math&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo&gt;⊆&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; such that any injective continuous commutativity and spectrum preserving map &lt;span&gt;&lt;math&gt;&lt;mi&gt;ϕ&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 1","pages":"Article 129497"},"PeriodicalIF":1.2,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683951","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":"Null controllability for cascade systems of coupled backward stochastic parabolic equations with one distributed control","authors":"Said Boulite ,&nbsp;Abdellatif Elgrou ,&nbsp;Lahcen Maniar","doi":"10.1016/j.jmaa.2025.129489","DOIUrl":"10.1016/j.jmaa.2025.129489","url":null,"abstract":"<div><div>We prove the null controllability of a cascade system of <em>n</em> coupled backward stochastic parabolic equations, which involve both reaction and convection terms, as well as general second-order parabolic operators, with <span><math><mi>n</mi><mo>≥</mo><mn>2</mn></math></span>. To achieve this, we apply a single distributed control to the first equation, while the other equations are controlled through the coupling. To obtain our results, we develop a new global Carleman estimate for the forward stochastic parabolic adjoint system, with some terms in the <span><math><msup><mrow><mi>H</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></math></span>-space. Subsequently, we derive the corresponding observability inequality, and using the classical duality argument, we establish our null controllability result. Additionally, we provide an accurate estimate for the null control cost in terms of the final time <em>T</em> and the potentials of the system.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 2","pages":"Article 129489"},"PeriodicalIF":1.2,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143684951","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":"Adjointable maps between linear orthosets","authors":"Jan Paseka ,&nbsp;Thomas Vetterlein","doi":"10.1016/j.jmaa.2025.129494","DOIUrl":"10.1016/j.jmaa.2025.129494","url":null,"abstract":"<div><div>Given an (anisotropic) Hermitian space <em>H</em>, the collection <span><math><mi>P</mi><mo>(</mo><mi>H</mi><mo>)</mo></math></span> of at most one-dimensional subspaces of <em>H</em>, equipped with the orthogonal relation ⊥ and the zero linear subspace {0}, is a linear orthoset and up to orthoisomorphism any linear orthoset of rank ⩾4 arises in this way. We investigate in this paper the correspondence of structure-preserving maps between Hermitian spaces on the one hand and between the associated linear orthosets on the other hand. Our particular focus is on adjointable maps.</div><div>We show that, under a mild assumption, adjointable maps between linear orthosets are induced by quasilinear maps between Hermitian spaces and if the latter are linear, they are adjointable as well. Specialised versions of this correlation lead to Wigner-type theorems; we see, for instance, that orthoisomorphisms between the orthosets associated with at least 3-dimensional Hermitian spaces are induced by quasiunitary maps.</div><div>In addition, we point out that orthomodular spaces of dimension ⩾4 can be characterised as irreducible Fréchet orthosets such that the inclusion map of any subspace is adjointable. Together with a transitivity condition, we may in this way describe the infinite-dimensional classical Hilbert spaces.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 1","pages":"Article 129494"},"PeriodicalIF":1.2,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143679334","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":"Monotonicity and symmetry of solutions for the fractional g-Laplacian equation","authors":"Xueying Chen","doi":"10.1016/j.jmaa.2025.129479","DOIUrl":"10.1016/j.jmaa.2025.129479","url":null,"abstract":"<div><div>In this paper, we focus on the fractional <em>g</em>-Laplacian equation<span><span><span><math><msup><mrow><mo>(</mo><mo>−</mo><msub><mrow><mi>Δ</mi></mrow><mrow><mi>g</mi></mrow></msub><mo>)</mo></mrow><mrow><mi>s</mi></mrow></msup><mi>u</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>∇</mi><mi>u</mi><mo>)</mo></math></span></span></span> in a bounded domain which is strictly convex in the <span><math><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>-direction and symmetric about the plane <span><math><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mn>0</mn></math></span>. We also investigate the same equation in the whole space <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>. We implement the direct method of moving planes to obtain the monotonicity and symmetry of positive solutions in the <span><math><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>-direction.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"548 2","pages":"Article 129479"},"PeriodicalIF":1.2,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143642987","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}