Nonlinear Analysis-Theory Methods & Applications最新文献

{"title":"Fefferman–Stein type decomposition of CMO spaces in the Dunkl setting and an application","authors":"Qingdong Guo ,&nbsp;Ji Li ,&nbsp;Brett D. Wick","doi":"10.1016/j.na.2025.113916","DOIUrl":"10.1016/j.na.2025.113916","url":null,"abstract":"<div><div>In this paper, we establish the Fefferman–Stein type decomposition of the <span><math><mi>CMO</mi></math></span> space in the Dunkl setting. That is <span><math><mrow><mi>f</mi><mo>∈</mo><mi>CMO</mi><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>,</mo><mi>d</mi><mi>ω</mi><mo>)</mo></mrow></mrow></math></span> if and only if <span><span><span><math><mrow><mi>f</mi><mo>=</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>+</mo><munderover><mrow><mo>∑</mo></mrow><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>d</mi></mrow></munderover><msub><mrow><mover><mrow><mi>R</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mi>j</mi></mrow></msub><msub><mrow><mi>f</mi></mrow><mrow><mi>j</mi></mrow></msub><mo>,</mo></mrow></math></span></span></span>where <span><math><mrow><msub><mrow><mi>f</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>d</mi></mrow></msub><mo>∈</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msub><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span> and <span><math><msub><mrow><mover><mrow><mi>R</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mi>j</mi></mrow></msub></math></span>, <span><math><mrow><mi>j</mi><mo>=</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>d</mi></mrow></math></span>, represent the Dunkl–Riesz transforms. Our main tool is to characterize <span><math><mrow><mi>CMO</mi><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>,</mo><mi>d</mi><mi>ω</mi><mo>)</mo></mrow></mrow></math></span> via two approximations, which are new even for the classical space <span><math><mrow><mi>CMO</mi><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span>. As a direct application of our characterization of <span><math><mrow><mi>CMO</mi><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>,</mo><mi>d</mi><mi>ω</mi><mo>)</mo></mrow></mrow></math></span>, we prove the duality of <span><math><mrow><mi>CMO</mi><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>,</mo><mi>d</mi><mi>ω</mi><mo>)</mo></mrow></mrow></math></span> with <span><math><mrow><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>,</mo><mi>d</mi><mi>ω</mi><mo>)</mo></mrow></mrow></math></span>.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"262 ","pages":"Article 113916"},"PeriodicalIF":1.3,"publicationDate":"2025-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144829845","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On dimension-free and potential-free estimates for Riesz transforms associated with Schrödinger operators","authors":"Jacek Dziubański","doi":"10.1016/j.na.2025.113918","DOIUrl":"10.1016/j.na.2025.113918","url":null,"abstract":"<div><div>Let <span><math><mrow><mi>L</mi><mo>=</mo><mo>−</mo><mi>Δ</mi><mo>+</mo><mi>V</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> be a Schrödinger operator on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>, where <span><math><mrow><mi>V</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>≥</mo><mn>0</mn></mrow></math></span>, <span><math><mrow><mi>V</mi><mo>∈</mo><msubsup><mrow><mi>L</mi></mrow><mrow><mi>loc</mi></mrow><mrow><mn>1</mn></mrow></msubsup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span>. We give a short proof of dimension free <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span>-estimates, <span><math><mrow><mn>1</mn><mo>&lt;</mo><mi>p</mi><mo>≤</mo><mn>2</mn></mrow></math></span>, <span><math><mrow><mi>d</mi><mo>≥</mo><mn>3</mn></mrow></math></span>, for the vector of the Riesz transforms <span><math><mrow><mrow><mo>(</mo><mrow><mfrac><mrow><mi>∂</mi></mrow><mrow><mi>∂</mi><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></mfrac><msup><mrow><mi>L</mi></mrow><mrow><mo>−</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup><mo>,</mo><mfrac><mrow><mi>∂</mi></mrow><mrow><mi>∂</mi><msub><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></mfrac><msup><mrow><mi>L</mi></mrow><mrow><mo>−</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup><mo>,</mo><mo>…</mo><mo>,</mo><mfrac><mrow><mi>∂</mi></mrow><mrow><mi>∂</mi><msub><mrow><mi>x</mi></mrow><mrow><mi>d</mi></mrow></msub></mrow></mfrac><msup><mrow><mi>L</mi></mrow><mrow><mo>−</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></mrow><mo>)</mo></mrow><mo>.</mo></mrow></math></span> The constant in the estimates does not depend on the potential <span><math><mi>V</mi></math></span>. We simultaneously provide a short proof of the weak-type <span><math><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></math></span> estimates for <span><math><mrow><mfrac><mrow><mi>∂</mi></mrow><mrow><mi>∂</mi><msub><mrow><mi>x</mi></mrow><mrow><mi>j</mi></mrow></msub></mrow></mfrac><msup><mrow><mi>L</mi></mrow><mrow><mo>−</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></mrow></math></span>.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"262 ","pages":"Article 113918"},"PeriodicalIF":1.3,"publicationDate":"2025-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144842243","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The superposition principle for local 1-dimensional currents","authors":"L. Ambrosio,&nbsp;F. Renzi,&nbsp;F. Vitillaro","doi":"10.1016/j.na.2025.113913","DOIUrl":"10.1016/j.na.2025.113913","url":null,"abstract":"<div><div>We prove that every one-dimensional locally normal metric current, intended in the sense of U. Lang and S. Wenger, admits a nice integral representation through currents associated to (possibly unbounded) curves with locally finite length, generalizing the result shown by E. Paolini and E. Stepanov in the special case of Ambrosio–Kirchheim normal currents. Our result holds in Polish spaces, or more generally in complete metric spaces for 1-currents with tight support.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"262 ","pages":"Article 113913"},"PeriodicalIF":1.3,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144809686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Convergence of normalizations for partially integrable differential systems","authors":"Wenyong Huang ,&nbsp;Valery G. Romanovski ,&nbsp;Xiang Zhang","doi":"10.1016/j.na.2025.113902","DOIUrl":"10.1016/j.na.2025.113902","url":null,"abstract":"<div><div>This paper provides some criteria to characterize convergence of normalizations which transform partially integrable analytic differential systems to their Poincaré–Dulac normal forms. For a family of four-dimensional partially integrable differential systems near an equilibrium which has one pair of conjugate imaginary eigenvalues and a pair of resonant nonzero real eigenvalues, we prove convergence of their normalizations. For analytic differential systems with dimension larger than 4, we illustrate that partial integrability may not be sufficient to ensure convergence of the normalizations even though Bruno’s condition <span><math><mi>ω</mi></math></span> holds. This work generalizes in a natural way the classical results by Poincaré and Lyapunov for a monodromic equilibrium, as well as the one by Moser for a hyperbolic saddle of analytic Hamiltonian systems of one degree of freedom.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"262 ","pages":"Article 113902"},"PeriodicalIF":1.3,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144779749","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Minimizers of mass-constrained functionals involving a nonattractive point interaction","authors":"Gustavo de Paula Ramos","doi":"10.1016/j.na.2025.113905","DOIUrl":"10.1016/j.na.2025.113905","url":null,"abstract":"<div><div>We establish conditions to ensure the existence of minimizer for a class of mass-constrained functionals involving a nonattractive point interaction in three dimensions. The existence of minimizers follows from the compactness of minimizing sequences which holds when we can simultaneously rule out the possibilities of vanishing and dichotomy. The proposed method is derived from the strategy used to avoid vanishing in Adami et al. (2022) and the strategy used to avoid dichotomy in Bellazzini and Siciliano (2011). As applications, we prove the existence of ground states with sufficiently small mass for the following nonlinear problems with a point interaction: a Kirchhoff-type equation and the Schrödinger–Poisson system.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"262 ","pages":"Article 113905"},"PeriodicalIF":1.3,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144779748","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Higher order expansion at infinity of solutions for Monge–Ampère equations in the half space","authors":"Lichun Liang","doi":"10.1016/j.na.2025.113912","DOIUrl":"10.1016/j.na.2025.113912","url":null,"abstract":"<div><div>In this paper, we investigate the asymptotic behavior of viscosity solutions for Monge–Ampère equations in the half space with a Dirichlet boundary condition on the flat boundary. Via the Kelvin transform, we characterize the asymptotic remainders by a single function near the origin. Such a function is smooth in the neighborhood of the origin in even dimension, but only <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn><mo>,</mo><mi>α</mi></mrow></msup></math></span> <span><math><mrow><mo>(</mo><mn>0</mn><mo>&lt;</mo><mi>α</mi><mo>&lt;</mo><mn>1</mn><mo>)</mo></mrow></math></span> in odd dimension.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"262 ","pages":"Article 113912"},"PeriodicalIF":1.3,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144779750","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Existence of positive solutions for nonlinear elliptic equations with critical growth on exterior domains","authors":"Ting-Ting Dai,&nbsp;Zeng-Qi Ou,&nbsp;Chun-Lei Tang,&nbsp;Ying Lv","doi":"10.1016/j.na.2025.113911","DOIUrl":"10.1016/j.na.2025.113911","url":null,"abstract":"<div><div>In this paper, we prove the existence of solutions for nonlinear elliptic equation with critical growth <span><math><mfenced><mrow><mtable><mtr><mtd></mtd><mtd><msup><mrow><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow></mrow><mrow><mi>s</mi></mrow></msup><mi>u</mi><mo>+</mo><mi>V</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>u</mi><mo>=</mo><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><msubsup><mrow><mn>2</mn></mrow><mrow><mi>s</mi></mrow><mrow><mo>∗</mo></mrow></msubsup><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi></mtd><mtd><mtext>in</mtext><mspace></mspace><mi>Ω</mi><mo>,</mo></mtd></mtr><mtr><mtd></mtd><mtd><mi>u</mi><mo>=</mo><mn>0</mn></mtd><mtd><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> where <span><math><mrow><mi>s</mi><mo>∈</mo><mrow><mo>(</mo></mrow><mn>0</mn><mo>,</mo><mn>1</mn><mrow><mo>]</mo></mrow><mo>,</mo><mi>N</mi><mo>&gt;</mo><mn>2</mn><mi>s</mi></mrow></math></span>, and <span><math><mrow><msubsup><mrow><mn>2</mn></mrow><mrow><mi>s</mi></mrow><mrow><mo>∗</mo></mrow></msubsup><mo>=</mo><mfrac><mrow><mn>2</mn><mi>N</mi></mrow><mrow><mi>N</mi><mo>−</mo><mn>2</mn><mi>s</mi></mrow></mfrac></mrow></math></span> is the critical Sobolev exponent. Here, <span><math><mrow><mi>V</mi><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mfrac><mrow><mi>N</mi></mrow><mrow><mn>2</mn><mi>s</mi></mrow></mfrac></mrow></msup><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow></mrow></math></span> is a given nonnegative potential, <span><math><msup><mrow><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow></mrow><mrow><mi>s</mi></mrow></msup></math></span> denotes the fractional Laplace operator, <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 exterior domain with smooth boundary <span><math><mrow><mi>∂</mi><mi>Ω</mi><mo>≠</mo><mo>0̸</mo></mrow></math></span> such that <span><math><mrow><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>∖</mo><mi>Ω</mi></mrow></math></span> non-empty and bounded. Using barycentric functions and the minimax method, we establish the existence of a positive solution <span><math><mrow><mi>u</mi><mo>∈</mo><msubsup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>s</mi><mo>,</mo><mn>2</mn></mrow></msubsup><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow></mrow></math></span> under the assumption that <span><math><mrow><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>∖</mo><mi>Ω</mi></mrow></math></span> is contained in a sufficiently small ball.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"262 ","pages":"Article 113911"},"PeriodicalIF":1.3,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144779652","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Scattering for the quartic generalized Benjamin–Bona–Mahony equation","authors":"A. George Morgan","doi":"10.1016/j.na.2025.113909","DOIUrl":"10.1016/j.na.2025.113909","url":null,"abstract":"<div><div>The generalized Benjamin–Bona–Mahony equation (gBBM) models nonlinear waves in dispersive media. In the long-wave limit, gBBM is approximately equivalent to the generalized Korteweg–de Vries equation (gKdV). While the long-time behaviour of small solutions to gKdV is well-understood, the corresponding theory for gBBM has progressed little since the 1990s. Using a space–time resonance approach, I establish linear dispersive decay and scattering for small solutions to the quartic-nonlinear gBBM. To my knowledge, this result provides the first global-in-time pointwise estimates on small solutions to gBBM with a nonlinear power less than or equal to five. Owing to nonzero inflection points in the linearized gBBM dispersion relation, there exist isolated space–time resonances without null structure, but in the course of the proof I show these resonances do not obstruct scattering.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"261 ","pages":"Article 113909"},"PeriodicalIF":1.3,"publicationDate":"2025-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144757567","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Boundary regularity for nonlocal elliptic equations over Reifenberg flat domains","authors":"Adriano Prade","doi":"10.1016/j.na.2025.113908","DOIUrl":"10.1016/j.na.2025.113908","url":null,"abstract":"<div><div>We prove sharp boundary regularity of solutions to nonlocal elliptic equations arising from operators comparable to the fractional Laplacian over Reifenberg flat sets and with null exterior condition. More precisely, if the operator has order <span><math><mrow><mn>2</mn><mi>s</mi></mrow></math></span> then the solution is <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>s</mi><mo>−</mo><mi>ɛ</mi></mrow></msup></math></span> regular for all <span><math><mrow><mi>ɛ</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span> provided the flatness parameter is small enough. The proof relies on an induction argument and its main ingredients are the construction of a suitable barrier and the comparison principle.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"261 ","pages":"Article 113908"},"PeriodicalIF":1.3,"publicationDate":"2025-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144757568","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fractional Chern–Simons–Higgs models on finite graphs via a topological degree approach","authors":"Chunlian Liu ,&nbsp;Ziyi Chen ,&nbsp;Linfeng Wang","doi":"10.1016/j.na.2025.113910","DOIUrl":"10.1016/j.na.2025.113910","url":null,"abstract":"<div><div>We investigate the fractional Chern–Simons–Higgs models of the form <span><span><span><math><mrow><msup><mrow><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow></mrow><mrow><mi>s</mi></mrow></msup><mi>u</mi><mo>=</mo><mi>λ</mi><msup><mrow><mi>e</mi></mrow><mrow><mi>u</mi></mrow></msup><msup><mrow><mrow><mo>(</mo><msup><mrow><mi>e</mi></mrow><mrow><mi>u</mi></mrow></msup><mo>−</mo><mn>1</mn><mo>)</mo></mrow></mrow><mrow><mn>2</mn><mi>p</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>f</mi></mrow></math></span></span></span>on a connected finite graph, where <span><math><msup><mrow><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow></mrow><mrow><mi>s</mi></mrow></msup></math></span> is the fractional Laplace operator, <span><math><mrow><mi>s</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>, <span><math><mi>λ</mi></math></span> is a real number, <span><math><mi>p</mi></math></span> is a non-negative integer, and <span><math><mi>f</mi></math></span> is a function on the graph. We focus on the fractional Laplace operator defined with heat kernels and employ the topological degree theory as our main tool. First, we prove that all solutions to fractional Chern–Simons–Higgs models are uniformly bounded. Second, we calculate the topological degree by discussing the existence of the solution to a homotopy equation case by case. As consequences, we obtain the existence results for the fractional Chern–Simons–Higgs models on a connected finite graph.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"261 ","pages":"Article 113910"},"PeriodicalIF":1.3,"publicationDate":"2025-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144757566","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}