Journal of Mathematical Analysis and Applications最新文献

{"title":"A note on zeros of derivatives of ultraspherical Bessel functions","authors":"Tao Jiang","doi":"10.1016/j.jmaa.2026.130483","DOIUrl":"10.1016/j.jmaa.2026.130483","url":null,"abstract":"<div><div>For any fixed <span><math><mi>ν</mi><mo>≥</mo><mn>0</mn><mo>,</mo><mi>δ</mi><mo>∈</mo><mi>R</mi></math></span> and <span><math><mi>x</mi><mo>&gt;</mo><mn>0</mn></math></span>, we investigate the positive zeros of the derivatives <span><math><msubsup><mrow><mi>j</mi></mrow><mrow><mi>ν</mi><mo>,</mo><mi>δ</mi></mrow><mrow><mo>′</mo></mrow></msubsup><mo>(</mo><mi>x</mi><mo>)</mo></math></span> and <span><math><msubsup><mrow><mi>y</mi></mrow><mrow><mi>ν</mi><mo>,</mo><mi>δ</mi></mrow><mrow><mo>′</mo></mrow></msubsup><mo>(</mo><mi>x</mi><mo>)</mo></math></span>, where<span><span><span><math><msub><mrow><mi>j</mi></mrow><mrow><mi>ν</mi><mo>,</mo><mi>δ</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><msup><mrow><mi>x</mi></mrow><mrow><mo>−</mo><mi>δ</mi></mrow></msup><msub><mrow><mi>J</mi></mrow><mrow><mi>ν</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo><mspace></mspace><mtext>and</mtext><mspace></mspace><msub><mrow><mi>y</mi></mrow><mrow><mi>ν</mi><mo>,</mo><mi>δ</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><msup><mrow><mi>x</mi></mrow><mrow><mo>−</mo><mi>δ</mi></mrow></msup><msub><mrow><mi>Y</mi></mrow><mrow><mi>ν</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>)</mo><mo>.</mo></math></span></span></span> We derive asymptotic expansions for their <em>k</em>-th positive zeros as <span><math><mi>k</mi><mo>→</mo><mo>∞</mo></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 2","pages":"Article 130483"},"PeriodicalIF":1.2,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174690","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":"Interior pointwise C1 and C1,1 regularity of solutions for general semilinear elliptic equation in nondivergence form","authors":"Jingqi Liang","doi":"10.1016/j.jmaa.2026.130462","DOIUrl":"10.1016/j.jmaa.2026.130462","url":null,"abstract":"<div><div>In this paper, we obtain <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> and <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msup></math></span> regularity of <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>-viscosity solutions for general semilinear elliptic equation in nondivergence form under some more weaker assumptions, which generalize the result for equations with nonhomogeneous term <span><math><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span> to <span><math><mi>f</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>)</mo></math></span>. In particular, the nonhomogeneous term <span><math><mi>f</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>)</mo></math></span> is assumed optimally to satisfy uniform Dini continuity condition in <em>u</em> and modified <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msup></math></span> Newtonian potential condition in <em>x</em>. For unbounded coefficients, if <span><math><msub><mrow><mi>a</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub></math></span> is <span><math><msubsup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow><mrow><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msubsup></math></span> at <span><math><msub><mrow><mi>x</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><mi>Ω</mi></math></span> with small modulus, <span><math><msub><mrow><mi>b</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msup><mo>(</mo><mi>Ω</mi><mo>)</mo></math></span> for some <span><math><mi>q</mi><mo>&gt;</mo><mi>n</mi></math></span>, the solution is <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> at <span><math><msub><mrow><mi>x</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>. Furthermore, if <span><math><msub><mrow><mi>a</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo>,</mo><mspace></mspace><msub><mrow><mi>b</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> are Dini continuous at <span><math><msub><mrow><mi>x</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>, the solution is <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msup></math></span> at <span><math><msub><mrow><mi>x</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 2","pages":"Article 130462"},"PeriodicalIF":1.2,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174654","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":"Elliptic orthogonal polynomials and OPRL","authors":"Victor Alves ,&nbsp;Andrei Martínez-Finkelshtein","doi":"10.1016/j.jmaa.2026.130461","DOIUrl":"10.1016/j.jmaa.2026.130461","url":null,"abstract":"<div><div>We explore a class of meromorphic functions on elliptic curves, termed <em>elliptic orthogonal a-polynomials</em> (<em>a</em>-EOPs), which extend the classical notion of orthogonal polynomials to compact Riemann surfaces of genus one. Building on Bertola's construction of orthogonal sections, we study these functions via non-Hermitian orthogonality on the torus, establish their recurrence properties, and derive an analogue of the Christoffel–Darboux formula. We demonstrate that, under real-valued orthogonality conditions, <em>a</em>-EOPs exhibit interlacing and simplicity of zeros similar to orthogonal polynomials on the real line (OPRL). Furthermore, we construct a general correspondence between families of OPRL and elliptic orthogonal functions, including a decomposition into multiple orthogonality relations, and identify new interlacing phenomena induced by rational deformations of the orthogonality weight.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 2","pages":"Article 130461"},"PeriodicalIF":1.2,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174658","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":"Optimal meshes for weighted multivariate polynomials in Rd","authors":"András Kroó","doi":"10.1016/j.jmaa.2026.130542","DOIUrl":"10.1016/j.jmaa.2026.130542","url":null,"abstract":"<div><div>In this paper we consider the problem of discretization of uniform norm on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> of weighted algebraic polynomials. Discretization of uniform norm for elements of linear subspaces <span><math><msub><mrow><mi>U</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>⊂</mo><mi>C</mi><mo>(</mo><mi>K</mi><mo>)</mo><mo>,</mo><mi>n</mi><mo>∈</mo><mi>N</mi></math></span> bounded on <em>K</em> consists in finding sets <span><math><msub><mrow><mi>Y</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>⊂</mo><mi>K</mi></math></span> of asymptotically optimal cardinality <span><math><mrow><mi>card</mi></mrow><msub><mrow><mi>Y</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>∼</mo><mrow><mi>dim</mi></mrow><msub><mrow><mi>U</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> such that with some <span><math><mi>c</mi><mo>&gt;</mo><mn>0</mn></math></span> independent of <em>n</em> we have <span><math><msub><mrow><mo>‖</mo><mi>p</mi><mo>‖</mo></mrow><mrow><mi>K</mi></mrow></msub><mo>≤</mo><mi>c</mi><msub><mrow><mo>‖</mo><mi>p</mi><mo>‖</mo></mrow><mrow><msub><mrow><mi>Y</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></msub><mo>,</mo><mspace></mspace><mspace></mspace><mo>∀</mo><mi>p</mi><mo>∈</mo><msub><mrow><mi>U</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>,</mo><mspace></mspace><mspace></mspace><mi>n</mi><mo>∈</mo><mi>N</mi></math></span>. We will consider weighted polynomial spaces <span><math><msub><mrow><mi>U</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>=</mo><msup><mrow><mi>w</mi></mrow><mrow><mi>n</mi></mrow></msup><msubsup><mrow><mi>P</mi></mrow><mrow><mi>n</mi></mrow><mrow><mi>d</mi></mrow></msubsup></math></span> with <span><math><msubsup><mrow><mi>P</mi></mrow><mrow><mi>n</mi></mrow><mrow><mi>d</mi></mrow></msubsup></math></span> being the set of algebraic polynomials of <em>d</em> variables and degree ≤<em>n</em> and show that under some mild growth conditions imposed on the weight <em>w</em> explicit optimal meshes can be constructed on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 2","pages":"Article 130542"},"PeriodicalIF":1.2,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147385480","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":"Multiple symmetric periodic solutions of distributed delay differential systems via Hamiltonian systems","authors":"Yuyou Zhong ,&nbsp;Qi Wang ,&nbsp;Chungen Liu","doi":"10.1016/j.jmaa.2026.130464","DOIUrl":"10.1016/j.jmaa.2026.130464","url":null,"abstract":"<div><div>In this paper, we investigate a class of non-autonomous high-dimensional differential systems with distributed delay. By exploiting the equivalence between finding periodic solutions for such systems under symmetric boundary conditions and solving an associated first-order Hamiltonian system, we establish novel multiplicity results. These results are obtained through a combination of symmetric index theory and critical point theory.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 2","pages":"Article 130464"},"PeriodicalIF":1.2,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146057485","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":"Legendre curve shortening flow in the unit circle bundle of R2","authors":"Mingyan Li","doi":"10.1016/j.jmaa.2026.130479","DOIUrl":"10.1016/j.jmaa.2026.130479","url":null,"abstract":"<div><div>Motivated by Legendre curves in 3-dimensional Sasaki manifolds, in this note we study Legendre curves in the unit circle bundle <span><math><msub><mrow><mi>T</mi></mrow><mrow><mn>1</mn></mrow></msub><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> of <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>, which is a contact manifold, but not a Sasaki manifold. We introduce a curve shortening flow in <span><math><msub><mrow><mi>T</mi></mrow><mrow><mn>1</mn></mrow></msub><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and show that it is a fourth order flow that preserves the Legendre condition and decreases the length energy. The well-posedness of this flow is proved.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 2","pages":"Article 130479"},"PeriodicalIF":1.2,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174692","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":"Exact and τ-method approximate solutions to a two-phase Stefan problem with Robin condition and exponential sources","authors":"Julieta Bollati ,&nbsp;María F. Natale ,&nbsp;José A. Semitiel ,&nbsp;Domingo A. Tarzia","doi":"10.1016/j.jmaa.2026.130458","DOIUrl":"10.1016/j.jmaa.2026.130458","url":null,"abstract":"<div><div>This work examines a two-phase Stefan problem in a semi-infinite domain with a convective (Robin-type) boundary condition at the fixed face and with exponential internal heat sources in terms of a similarity-type variable. Existence and uniqueness of the similarity-type solution are established with exactness, and asymptotic analysis of the system is carried out, showing convergence towards the associated two-phase Stefan problem with the imposed temperature condition at the fixed face in the limit when the heat transfer coefficient tends to infinity. A numerical example pertaining to melting paraffin is given to support the theoretical results. Moreover, the Tau-method based on shifted Chebyshev and Legendre polynomials are employed to construct approximate solutions that are then compared to the exact similarity-type solution that serves as benchmark for quantifying the accuracy of spectral approximations.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 2","pages":"Article 130458"},"PeriodicalIF":1.2,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146174656","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 solutions for ordinary differential inclusions with periodic boundary conditions","authors":"Eleonora Amoroso,&nbsp;Gabriele Bonanno,&nbsp;Giuliano Klun,&nbsp;Valeria Morabito","doi":"10.1016/j.jmaa.2026.130533","DOIUrl":"10.1016/j.jmaa.2026.130533","url":null,"abstract":"<div><div>By employing variational methods for nonsmooth functionals, we establish the existence of two distinct solutions to an ordinary differential problem characterized by a set-valued reaction term. The investigation is conducted under the framework of periodic boundary conditions, which introduces additional challenges in the application of variational techniques due to the presence of nonsmooth functionals and the set-valued nature of the nonlinearity.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 2","pages":"Article 130533"},"PeriodicalIF":1.2,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147385478","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 problem for higher order operators and operators of logarithmic type via renormalization","authors":"David Lee","doi":"10.1016/j.jmaa.2026.130510","DOIUrl":"10.1016/j.jmaa.2026.130510","url":null,"abstract":"<div><div>We introduce a method of obtaining a higher order extension problem, á la Caffarelli-Silvestre, utilizing ideas from renormalization. Moreover, we give an alternative perspective of the recently developed extension problem for the logarithmic laplacian developed by Chen, Hauer and Weth (2023) [<span><span>arXiv:2312.15689</span><svg><path></path></svg></span>].</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 2","pages":"Article 130510"},"PeriodicalIF":1.2,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147385620","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":"Energy conservation for weak solution of incompressible viscoelastic fluids in bounded domain","authors":"Long Guo,&nbsp;Jingyu Jia","doi":"10.1016/j.jmaa.2026.130454","DOIUrl":"10.1016/j.jmaa.2026.130454","url":null,"abstract":"<div><div>In this paper, we study the energy conservation of weak solution to the incompressible viscoelastic equations in a bounded domain. When the coefficient of viscosity <span><math><mi>μ</mi><mo>=</mo><mn>0</mn></math></span>, energy equality is proved under some global Hölder regularity condition for the velocity <strong><em>u</em></strong> and deformation tensor <strong><em>F</em></strong>. When <span><math><mi>μ</mi><mo>&gt;</mo><mn>0</mn></math></span>, we proved that some global integrability condition for <span><math><mo>(</mo><mi>u</mi><mo>,</mo><mi>F</mi><mo>)</mo></math></span> and suitable integrability conditions near the boundary for the pressure <em>p</em> are sufficient for the energy equality.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"559 2","pages":"Article 130454"},"PeriodicalIF":1.2,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146057486","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}