Journal of Mathematical Analysis and Applications最新文献

{"title":"Global solutions to the higher-dimensional chemotaxis-consumption system","authors":"Wenping Du","doi":"10.1016/j.jmaa.2025.129540","DOIUrl":"10.1016/j.jmaa.2025.129540","url":null,"abstract":"<div><div>This paper is devoted to a parabolic-parabolic chemotaxis-consumption PDE's system with singular sensitivity under homogeneous Neumann boundary conditions in a smoothly bounded 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>2</mn></math></span>. We consider a growth term of logistic type in the equation of “<em>u</em>” in the form <span><math><msup><mrow><mi>u</mi></mrow><mrow><mi>α</mi></mrow></msup><mo>(</mo><mn>1</mn><mo>−</mo><msub><mrow><mo>∫</mo></mrow><mrow><mi>Ω</mi></mrow></msub><msup><mrow><mi>u</mi></mrow><mrow><mi>β</mi></mrow></msup><mo>)</mo></math></span>. We provide conditions to ensure global existence of solutions. As compared to previous mathematical studies, the novelty (also is difficulty) of this problem arises from the combination of the singular sensitivity and the nonlocal nonlinear reaction.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 1","pages":"Article 129540"},"PeriodicalIF":1.2,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143760678","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":"Homoclinic solutions for a class of second-order singular Hamiltonian systems","authors":"Morched Boughariou ,&nbsp;Marouen Mahmoud","doi":"10.1016/j.jmaa.2025.129535","DOIUrl":"10.1016/j.jmaa.2025.129535","url":null,"abstract":"<div><div>We consider a class of singular second-order Hamiltonian systems in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>(</mo><mi>N</mi><mo>≥</mo><mn>2</mn><mo>)</mo></math></span><span><span><span><math><mover><mrow><mi>q</mi></mrow><mrow><mo>¨</mo></mrow></mover><mo>+</mo><mi>∇</mi><mi>V</mi><mo>(</mo><mi>q</mi><mo>)</mo><mo>=</mo><mn>0</mn><mo>,</mo><mspace></mspace><mi>q</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>∉</mo><mi>D</mi><mo>,</mo></math></span></span></span> where <span><math><mi>V</mi><mo>:</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>∖</mo><mi>D</mi><mo>→</mo><mi>R</mi></math></span> has a strict global maximum 0 at the origin and <em>D</em> ⊂  <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>∖</mo><mo>{</mo><mn>0</mn><mo>}</mo></math></span> is a set of singularities, that is, <span><math><mi>V</mi><mo>(</mo><mi>q</mi><mo>)</mo><mo>→</mo><mo>−</mo><mo>∞</mo></math></span> as <span><math><mrow><mi>dist</mi></mrow><mo>(</mo><mi>q</mi><mo>,</mo><mi>D</mi><mo>)</mo><mo>→</mo><mn>0</mn></math></span>. Under the condition that <em>D</em> is a compact set with <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-boundary and <span><math><mi>V</mi><mo>(</mo><mi>q</mi><mo>)</mo><mo>∼</mo><mo>−</mo><msup><mrow><mo>[</mo><mrow><mi>dist</mi></mrow><mo>(</mo><mi>q</mi><mo>,</mo><mi>D</mi><mo>)</mo><mo>]</mo></mrow><mrow><mo>−</mo><mi>α</mi></mrow></msup></math></span> as <span><math><mrow><mi>dist</mi></mrow><mo>(</mo><mi>q</mi><mo>,</mo><mi>D</mi><mo>)</mo><mo>→</mo><mn>0</mn></math></span> for some <span><math><mi>α</mi><mo>&gt;</mo><mn>0</mn></math></span>, we show the existence of a nontrivial homoclinic solution at 0 via a suitable approximation method.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 1","pages":"Article 129535"},"PeriodicalIF":1.2,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143760163","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 generating functions for partitions with repeated smallest part","authors":"George E. Andrews ,&nbsp;Mohamed El Bachraoui","doi":"10.1016/j.jmaa.2025.129537","DOIUrl":"10.1016/j.jmaa.2025.129537","url":null,"abstract":"<div><div>We consider the number of integer partitions whose smallest part is repeated exactly <em>k</em> times and the remaining parts are not repeated. We prove that their generating functions are linear combinations of the <em>q</em>-Pochhammer symbols with polynomials as coefficients. Focusing on the cases <span><math><mi>k</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn></math></span>, and 3, we derive new identities and inequalities for the partitions into distinct parts.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 1","pages":"Article 129537"},"PeriodicalIF":1.2,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143760162","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":"Upper bound on the blowup rate of inhomogeneous NLS with Aharonov-Bohm magnetic potential","authors":"Yuan Li","doi":"10.1016/j.jmaa.2025.129529","DOIUrl":"10.1016/j.jmaa.2025.129529","url":null,"abstract":"<div><div>In this paper, we consider the mass-supercritical inhomogeneous nonlinear Schrödinger equation with an Aharonov-Bohm magnetic potential in the two dimensional case and obtain an upper bound on the blowup rate in the non-radial case.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 2","pages":"Article 129529"},"PeriodicalIF":1.2,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143737769","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":"Exponential stabilization and minimization problem for a delayed semilinear system","authors":"Ayoub Cheddour,&nbsp;Abdelhai Elazzouzi","doi":"10.1016/j.jmaa.2025.129528","DOIUrl":"10.1016/j.jmaa.2025.129528","url":null,"abstract":"<div><div>In this study, a weaker condition is introduced to address the exponential stabilization of semilinear systems in Hilbert spaces. Compared to the entire state space, verification is made easier by this condition, which is defined on a subspace of the phase space and connected to the system's initial condition. Interestingly, the condition is easier to verify as the first condition's norm gets closer to zero. Furthermore, the method avoids the requirement to explicitly find the semigroup's form, which is frequently difficult in reality. Additionally, a minimization problem is taken into account, and it is proven that the optimal control exists and is unique, guaranteeing exponential stabilization. Numerical simulations are used to validate the theoretical results through two examples.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"548 2","pages":"Article 129528"},"PeriodicalIF":1.2,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759148","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":"From mating difficulty in prey to oscillations in both prey and predator populations: Bifurcations of a predator-prey system","authors":"Zhenliang Zhu ,&nbsp;Lan Zou","doi":"10.1016/j.jmaa.2025.129531","DOIUrl":"10.1016/j.jmaa.2025.129531","url":null,"abstract":"<div><div>We study the dynamics of a Leslie type predator-prey model with weak Allee effect in prey and Holling type IV functional response function, where the weak Allee effect arises from the difficulty in mating. We investigate the high degenerate bifurcations, including cusp type degenerate Bogdanov-Takens bifurcation of codimension 3, and focus type degenerate Bogdanov-Takens bifurcation of codimensions 3 and 4. The complicated dynamics of the system shows that weak Allee effect in prey might induce multiple steady states after some special predation interactions, and it also yields population oscillations. Furthermore, the cyclic amplitudes are sensitive on both parameters and initial values. Simulations also exhibit the qualitative results numerically.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 1","pages":"Article 129531"},"PeriodicalIF":1.2,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143760675","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":"The truncated multidimensional moment problem: Canonical solutions","authors":"Sergey Zagorodnyuk","doi":"10.1016/j.jmaa.2025.129524","DOIUrl":"10.1016/j.jmaa.2025.129524","url":null,"abstract":"<div><div>For the truncated multidimensional moment problem we introduce a notion of a canonical solution. Namely, canonical solutions are those solutions which are generated by commuting self-adjoint extensions inside the associated Hilbert space. It is constructed a 1-1 correspondence between canonical solutions and flat extensions of the given moments (both sets may be empty). In the case of the two-dimensional moment problem (with triangular truncations) a search for canonical solutions leads to an algebraic system of equations. A notion of the index <span><math><msub><mrow><mi>i</mi></mrow><mrow><mi>s</mi></mrow></msub></math></span> of nonself-adjointness for a set of prescribed moments is introduced. The case <span><math><msub><mrow><mi>i</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>=</mo><mn>0</mn></math></span> corresponds to flatness. In the case <span><math><msub><mrow><mi>i</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>=</mo><mn>1</mn></math></span> we get explicit necessary and sufficient conditions for the existence of canonical solutions. These conditions are valid for arbitrary sizes of truncations. In the case <span><math><msub><mrow><mi>i</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>=</mo><mn>2</mn></math></span> we get either explicit conditions for the existence of canonical solutions or a single quadratic equation with several unknowns. Numerical examples are provided.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 1","pages":"Article 129524"},"PeriodicalIF":1.2,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143760160","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":"Non-isometric translation and modulation invariant Hilbert spaces","authors":"P.K. Ratnakumar ,&nbsp;Joachim Toft ,&nbsp;Jasson Vindas","doi":"10.1016/j.jmaa.2025.129530","DOIUrl":"10.1016/j.jmaa.2025.129530","url":null,"abstract":"<div><div>Let <span><math><mi>H</mi></math></span> be a Hilbert space, continuously embedded in <span><math><msup><mrow><mi>S</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo></math></span>, and which contains at least one non-zero element in <span><math><msup><mrow><mi>S</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo></math></span>. If there is a constant <span><math><msub><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>&gt;</mo><mn>0</mn></math></span> such that<span><span><span><math><msub><mrow><mo>‖</mo><msup><mrow><mi>e</mi></mrow><mrow><mi>i</mi><mo>〈</mo><mspace></mspace><mo>⋅</mo><mspace></mspace><mo>,</mo><mi>ξ</mi><mo>〉</mo></mrow></msup><mi>f</mi><mo>(</mo><mspace></mspace><mo>⋅</mo><mspace></mspace><mo>−</mo><mi>x</mi><mo>)</mo><mo>‖</mo></mrow><mrow><mi>H</mi></mrow></msub><mo>≤</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msub><msub><mrow><mo>‖</mo><mi>f</mi><mo>‖</mo></mrow><mrow><mi>H</mi></mrow></msub><mo>,</mo><mspace></mspace><mi>f</mi><mo>∈</mo><mi>H</mi><mo>,</mo><mspace></mspace><mi>x</mi><mo>,</mo><mi>ξ</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>,</mo></math></span></span></span> then we prove that <span><math><mi>H</mi><mo>=</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo></math></span>, with equivalent norms.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 1","pages":"Article 129530"},"PeriodicalIF":1.2,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143760676","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":"Explicit bounds for Bell numbers and their ratios","authors":"Jerzy Grunwald,&nbsp;Grzegorz Serafin","doi":"10.1016/j.jmaa.2025.129527","DOIUrl":"10.1016/j.jmaa.2025.129527","url":null,"abstract":"<div><div>In this article, we provide a comprehensive analysis of the asymptotic behavior of Bell numbers, enhancing and unifying various results previously dispersed in the literature. We establish several explicit lower and upper bounds. The main results correspond to two asymptotic forms expressed by means of the Lambert <em>W</em> function. As an application, some straightforward elementary bounds are derived. Additionally, an absolute convergence rate of the ratio of consecutive Bell numbers is derived. One of the main challenges was to obtain satisfactory constants, as the Bell numbers grow rapidly, while the convergence rates are rather slow.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"549 2","pages":"Article 129527"},"PeriodicalIF":1.2,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143737770","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":"Existence and non-existence results for parabolic systems with an Hardy-Leray potential","authors":"Fatima Zohra Bengrine ,&nbsp;Ana Primo ,&nbsp;Giovanni Siclari","doi":"10.1016/j.jmaa.2025.129533","DOIUrl":"10.1016/j.jmaa.2025.129533","url":null,"abstract":"<div><div>In this paper we study the problem of existence or non existence of positive supersolution to the system<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><msub><mrow><mi>λ</mi></mrow><mrow><mn>1</mn></mrow></msub><mfrac><mrow><mi>u</mi></mrow><mrow><mo>|</mo><mi>x</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mo>+</mo><mi>f</mi><mo>(</mo><mi>v</mi><mo>,</mo><mi>∇</mi><mi>v</mi><mo>)</mo><mo>,</mo></mtd><mtd><mtext> in </mtext><msub><mrow><mi>Ω</mi></mrow><mrow><mi>T</mi></mrow></msub><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><msub><mrow><mi>λ</mi></mrow><mrow><mn>2</mn></mrow></msub><mfrac><mrow><mi>v</mi></mrow><mrow><mo>|</mo><mi>x</mi><msup><mrow><mo>|</mo></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mo>+</mo><mi>g</mi><mo>(</mo><mi>u</mi><mo>,</mo><mi>∇</mi><mi>u</mi><mo>)</mo><mo>,</mo></mtd><mtd><mtext> in </mtext><msub><mrow><mi>Ω</mi></mrow><mrow><mi>T</mi></mrow></msub><mo>,</mo></mtd></mtr></mtable></mrow></math></span></span></span> where <span><math><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>,</mo><mi>N</mi><mo>≥</mo><mn>3</mn></math></span>, is a regular domain containing the origin and:</div><div><em>i</em>) <span><math><mi>f</mi><mo>=</mo><msup><mrow><mi>v</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>,</mo><mi>g</mi><mo>=</mo><msup><mrow><mi>u</mi></mrow><mrow><mi>q</mi></mrow></msup></math></span>, <span><math><mi>i</mi><mi>i</mi><mo>)</mo></math></span> <span><math><mi>f</mi><mo>=</mo><mo>|</mo><mi>∇</mi><mi>v</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>p</mi></mrow></msup><mo>,</mo><mi>g</mi><mo>=</mo><mo>|</mo><mi>∇</mi><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>q</mi></mrow></msup></math></span>, <span><math><mi>i</mi><mi>i</mi><mi>i</mi><mo>)</mo></math></span> <span><math><mi>f</mi><mo>=</mo><msup><mrow><mi>v</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>,</mo><mi>g</mi><mo>=</mo><mo>|</mo><mi>∇</mi><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>q</mi></mrow></msup></math></span>.</div><div>According to the form of the nonlinearities, we are able to get the existence of critical curves separating the existence and the non existence regions. In the case <span><math><mi>f</mi><mo>=</mo><msup><mrow><mi>v</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> and <span><math><mi>g</mi><mo>=</mo><msup><mrow><mi>u</mi></mrow><mrow><mi>q</mi></mrow></msup></math></span>, we study the Cauchy system in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>×</mo><mo>(</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>)</mo></math></span>. The existence of a Fujita type exponent is deeply analyzed.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"550 1","pages":"Article 129533"},"PeriodicalIF":1.2,"publicationDate":"2025-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143760797","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}