Results in Applied Mathematics最新文献

{"title":"Weighted Lorentz estimates with a variable power for non-uniformly elliptic two-sided obstacle problems","authors":"Junjie Zhang,&nbsp;Lina Niu","doi":"10.1016/j.rinam.2025.100638","DOIUrl":"10.1016/j.rinam.2025.100638","url":null,"abstract":"<div><div>We proved an optimal local Calderón–Zygmund type estimate with a variable power in weighted Lorentz spaces for the weak solution of non-uniformly elliptic two-sided obstacle problems. It is mainly assumed that the nonlinearity satisfies the <span><math><mrow><mo>(</mo><mi>p</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>,</mo><mi>q</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>)</mo></mrow></math></span>-growth condition and <span><math><mrow><mo>(</mo><mi>δ</mi><mo>,</mo><mi>R</mi><mo>)</mo></mrow></math></span>-BMO condition, while the exponents <span><math><mrow><mi>p</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>,</mo><mi>q</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> are strong <span><math><mo>log</mo></math></span>-Hölder continuous functions. The approach of this paper is mainly based on the perturbation technique and maximal function free technique.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"28 ","pages":"Article 100638"},"PeriodicalIF":1.3,"publicationDate":"2025-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145060783","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Commutators of fractional maximal functions with Lipschitz functions on mixed-norm amalgam spaces","authors":"Suixin He ,&nbsp;Lihua Zhang ,&nbsp;Heng Yang","doi":"10.1016/j.rinam.2025.100628","DOIUrl":"10.1016/j.rinam.2025.100628","url":null,"abstract":"<div><div>In this paper, we investigate the commutators of fractional maximal functions on mixed-norm amalgam spaces. Furthermore, we present some new characterizations of Lipschitz functions.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100628"},"PeriodicalIF":1.3,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144864615","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Convergence analysis of a dual-wind discontinuous Galerkin method for an elliptic optimal control problem with control constraints","authors":"Satyajith Bommana Boyana ,&nbsp;Thomas Lewis ,&nbsp;Sijing Liu ,&nbsp;Yi Zhang","doi":"10.1016/j.rinam.2025.100624","DOIUrl":"10.1016/j.rinam.2025.100624","url":null,"abstract":"<div><div>This paper investigates a symmetric dual-wind discontinuous Galerkin (DWDG) method for solving an elliptic optimal control problem with control constraints. The governing constraint is an elliptic partial differential equation (PDE), which is discretized using the symmetric DWDG approach. We derive error estimates in the energy norm for both the state and the adjoint state, as well as in the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> norm of the control variable. Numerical experiments are provided to demonstrate the robustness and effectiveness of the developed scheme.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100624"},"PeriodicalIF":1.3,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144858193","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Smooth solitary waves for the generalized gKdV-4 equation","authors":"J. Noyola Rodriguez ,&nbsp;Cynthia G. Esquer-Pérez ,&nbsp;J.C. Hernández-Gómez ,&nbsp;Omar Rosario Cayetano","doi":"10.1016/j.rinam.2025.100625","DOIUrl":"10.1016/j.rinam.2025.100625","url":null,"abstract":"<div><div>We consider a generalization of KdV-type equations with a quartic nonlinearity <span><math><msup><mrow><mi>u</mi></mrow><mrow><mn>4</mn></mrow></msup></math></span> (gKdV-4), which includes dissipation terms similar to those appearing in the Benjamin-Bona-Mahoney equation as well as in the well-known Camassa–Holm and Degasperis-Procesi equations. Our objective is to construct classical solitary wave solutions (solitons-antisolitons) to this equation.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100625"},"PeriodicalIF":1.3,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144904587","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Analysis framework for stochastic predator–prey model with demographic noise","authors":"Louis Shuo Wang ,&nbsp;Jiguang Yu","doi":"10.1016/j.rinam.2025.100621","DOIUrl":"10.1016/j.rinam.2025.100621","url":null,"abstract":"<div><div>Most existing studies focus on environmental noise, with few studies focusing on pure demographic noise. We propose an analytical framework that applies stochastic differential equation tools to prove the well-posedness of solutions to such models with pure demographic noise and obtain moment and asymptotic bounds. We use this framework to prove that demographic noise does not lead to population extinction, and numerical results are consistent with it. Our proposed framework fills the gaps in research on the well-posedness and extinction impossibility of models with pure demographic noise and provides a rigorous mathematical framework for addressing a general ecology system in more sophisticated evolutionary setups.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100621"},"PeriodicalIF":1.3,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144864565","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Oscillation of generalized Riemann–Weber type differential equations with delay","authors":"Kazuki Ishibashi ,&nbsp;Shouki Miyauchi ,&nbsp;Housei Sakikawa","doi":"10.1016/j.rinam.2025.100637","DOIUrl":"10.1016/j.rinam.2025.100637","url":null,"abstract":"<div><div>In this study, we investigate the oscillatory behavior of a generalized Riemann–Weber type differential equation, incorporating a logarithmically varying perturbation term and a time delay. Specifically, we derive the precise conditions under which all non-trivial solutions of the considered equation oscillate when the effects of time delay and logarithmic perturbation act simultaneously. The oscillation constant, which determines the boundary between oscillatory and non-oscillatory behavior, coincides with that of the classical delayed equation. In particular, in the absence of a time delay, the generalized equation reduces to a known form, ensuring consistency with the existing theory.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100637"},"PeriodicalIF":1.3,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145026361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Turing patterns across geometries: A proven DSC-ETDRK4 solver from plane to sphere","authors":"Kolade M. Owolabi ,&nbsp;Edson Pindza ,&nbsp;Eben Maré","doi":"10.1016/j.rinam.2025.100631","DOIUrl":"10.1016/j.rinam.2025.100631","url":null,"abstract":"<div><div>This paper presents a unified and robust numerical framework that combines the Discrete Singular Convolution (DSC) method for spatial discretization with the Exponential Time Differencing Runge–Kutta (ETDRK4) scheme for temporal integration to solve reaction–diffusion systems. Specifically, we investigate the formation of Turing patterns – such as spots, stripes, and mixed structures – in classical models including the Gray–Scott, Brusselator, and Barrio–Varea–Aragón–Maini (BVAM) systems. The DSC method, employing the regularized Shannon’s delta kernel, delivers spectral-like accuracy in computing spatial derivatives on both regular and curved geometries. Coupled with the fourth-order ETDRK method, this approach enables efficient and stable time integration over long simulations. Importantly, we rigorously establish the necessary theoretical results – including convergence, stability, and consistency theorems, along with their proofs – for the combined DSC-ETDRK4 method when applied to both planar and curved surfaces. We demonstrate the capability of the proposed method to accurately reproduce and analyze complex spatiotemporal patterns on a variety of surfaces, including the plane, sphere, torus, and bumpy geometries. Numerical experiments confirm the method’s versatility, high accuracy, and computational efficiency, making it a powerful tool for the study of pattern formation in reaction–diffusion systems on diverse geometries.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100631"},"PeriodicalIF":1.3,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144893178","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multiplicity results for non-local operators of elliptic type","authors":"Emer Lopera ,&nbsp;Leandro Recôva ,&nbsp;Adolfo Rumbos","doi":"10.1016/j.rinam.2025.100626","DOIUrl":"10.1016/j.rinam.2025.100626","url":null,"abstract":"<div><div>In this paper, we study a class of problems proposed by Servadei and Valdinoci (2013); namely, <span><span><span>(1)</span><span><math><mfenced><mrow><mtable><mtr><mtd><mo>−</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>K</mi></mrow></msub><mi>u</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>−</mo><mi>λ</mi><mi>u</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mtd><mtd><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>)</mo></mrow><mo>,</mo><mtext>for</mtext><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>;</mo></mtd></mtr><mtr><mtd><mi>u</mi></mtd><mtd><mo>=</mo><mn>0</mn><mspace></mspace><mtext>in</mtext><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>∖</mo><mi>Ω</mi><mo>,</mo></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>where <span><math><mrow><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></mrow></math></span> is an open bounded set with Lipschitz boundary, <span><math><mrow><mi>λ</mi><mo>∈</mo><mi>R</mi></mrow></math></span>, <span><math><mrow><mi>f</mi><mo>∈</mo><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup><mrow><mo>(</mo><mover><mrow><mi>Ω</mi></mrow><mo>¯</mo></mover><mo>×</mo><mi>R</mi><mo>,</mo><mi>R</mi><mo>)</mo></mrow></mrow></math></span>, with <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mn>0</mn><mo>)</mo></mrow><mo>=</mo><mn>0</mn></mrow></math></span> for <span><math><mrow><mi>x</mi><mo>∈</mo><mi>Ω</mi></mrow></math></span>, and <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>K</mi></mrow></msub></math></span> is a non-local integrodifferential operator with homogeneous Dirichlet boundary condition. By computing the critical groups of the associated energy functional for problem <span><span>(1)</span></span> at the origin and at infinity, respectively, we prove that problem <span><span>(1)</span></span> has three nontrivial solutions for the case <span><math><mrow><mi>λ</mi><mo>&lt;</mo><msub><mrow><mi>λ</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></math></span> and two nontrivial solutions for the case <span><math><mrow><mi>λ</mi><mo>⩾</mo><msub><mrow><mi>λ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo></mrow></math></span> where <span><math><msub><mrow><mi>λ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> is the first eigenvalue of the operator <span><math><mrow><mo>−</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>K</mi></mrow></msub></mrow></math></span>. Finally, assuming that the nonlinearity <span><math><mi>f</mi></math></span> is odd in the second variable, we prove the existence of an unbounded sequence of weak solutions of problem <span><span>(1)</span></span> for the case <span><math><mrow><mi>λ</mi><mo>⩾</mo><msub><mrow><mi>λ</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></math></span>. We use variational methods and infinite-dimensional Morse theory to obtain the results.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100626"},"PeriodicalIF":1.3,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144852245","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Rational and singular points of a family of curves","authors":"M.C. Rodríguez-Palánquex","doi":"10.1016/j.rinam.2025.100630","DOIUrl":"10.1016/j.rinam.2025.100630","url":null,"abstract":"<div><div>This paper explores the properties of a family of absolutely irreducible projective plane curves, denoted <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>a</mi><mo>,</mo><mi>b</mi></mrow></msub></math></span>, which are defined over a finite field <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span> of characteristic 2. The curves are explicitly given by the homogeneous equation <span><math><mrow><msup><mrow><mi>Y</mi></mrow><mrow><mi>a</mi></mrow></msup><msup><mrow><mi>Z</mi></mrow><mrow><mi>b</mi><mo>−</mo><mi>a</mi></mrow></msup><mo>+</mo><mi>Y</mi><msup><mrow><mi>Z</mi></mrow><mrow><mi>b</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>+</mo><msup><mrow><mi>X</mi></mrow><mrow><mi>b</mi></mrow></msup><mo>=</mo><mn>0</mn></mrow></math></span>, where <span><math><mi>a</mi></math></span> and <span><math><mi>b</mi></math></span> are natural numbers satisfying the conditions <span><math><mrow><mi>a</mi><mo>≥</mo><mn>2</mn></mrow></math></span> and <span><math><mrow><mi>b</mi><mo>≥</mo><mi>a</mi></mrow></math></span>. A primary objective of the paper is to determine the number of rational points on these curves.</div><div>The work also includes a detailed analysis of the singular points of the curves, providing a classification of these points based on the parameters <span><math><mi>a</mi></math></span> and <span><math><mi>b</mi></math></span>. Furthermore, the relationship between the number of rational points and the genus of the curves is investigated, with specific computations carried out for curves defined over the finite field <span><math><msub><mrow><mi>F</mi></mrow><mrow><msup><mrow><mn>2</mn></mrow><mrow><mn>4</mn></mrow></msup></mrow></msub></math></span>. In particular, the paper presents explicit calculations of the number of rational points for curves of the form <span><math><msub><mrow><mi>C</mi></mrow><mrow><mn>2</mn><mo>,</mo><mi>b</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>C</mi></mrow><mrow><mn>3</mn><mo>,</mo><mi>b</mi></mrow></msub></math></span> over <span><math><msub><mrow><mi>F</mi></mrow><mrow><msup><mrow><mn>2</mn></mrow><mrow><mn>4</mn></mrow></msup></mrow></msub></math></span>, illustrating the connection between these counts and the genus of the curves.</div><div>This comprehensive analysis contributes to a deeper understanding of the arithmetic geometry of this family of curves over finite fields.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100630"},"PeriodicalIF":1.3,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144904588","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Enhanced PINNs for data-driven solitons and parameter discovery for (2+ 1)-dimensional coupled nonlinear Schrödinger systems","authors":"Hamid Momeni ,&nbsp;AllahBakhsh Yazdani Cherati ,&nbsp;Ali Valinejad","doi":"10.1016/j.rinam.2025.100635","DOIUrl":"10.1016/j.rinam.2025.100635","url":null,"abstract":"<div><div>This paper investigates data-driven solutions and parameter discovery to (2+ 1)-dimensional coupled nonlinear Schrödinger equations with variable coefficients (VC-CNLSEs), which describe transverse effects in optical fiber systems under perturbed dispersion and nonlinearity. By setting different forms of perturbation coefficients, we aim to recover the dark and anti-dark one- and two-soliton structures by employing an enhanced physics-based deep neural network algorithm, namely a physics-informed neural network (PINN). The enhanced PINN algorithm leverages the locally adaptive activation function mechanism to improve convergence speed and accuracy. In the lack of data acquisition, the PINN algorithms will enhance the capability of the neural networks by incorporating physical information into the training phase. We demonstrate that applying PINN algorithms to (2+ 1)-dimensional VC-CNLSEs requires distinct distributions of physical information. To address this, we propose a region-specific weighted loss function with the help of residual-based adaptive refinement strategy. In the meantime, we perform data-driven parameter discovery for the model equation, classified into two categories: constant coefficient discovery and variable coefficient discovery. For the former, we aim to predict the cross-phase modulation constant coefficient under varying noise intensities using enhanced PINN with a single neural network. For the latter, we employ a dual-network strategy to predict the dynamic behavior of the dispersion and nonlinearity perturbation functions. Our study demonstrates that the proposed framework holds significant potential for studying high-dimensional and complex solitonic dynamics in optical fiber systems.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"27 ","pages":"Article 100635"},"PeriodicalIF":1.3,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145010206","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}