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Meromorphic solutions of Bi-Fermat type partial differential and difference equations 比-费马型偏微分方程和差分方程的同态解
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-11-16 DOI: 10.1007/s13324-024-00989-w
Yingchun Gao, Kai Liu
{"title":"Meromorphic solutions of Bi-Fermat type partial differential and difference equations","authors":"Yingchun Gao,&nbsp;Kai Liu","doi":"10.1007/s13324-024-00989-w","DOIUrl":"10.1007/s13324-024-00989-w","url":null,"abstract":"<div><p>Fermat type functional equation with four terms </p><div><div><span>$$begin{aligned} f(z)^{n}+g(z)^{n}+h(z)^{n}+k(z)^{n}=1 end{aligned}$$</span></div></div><p>is difficult to solve completely even if <span>(n=2,3)</span>, in which the certain type of the above equation is also interesting and significant. In this paper, we first to consider the Bi-Fermat type quadratic partial differential equation </p><div><div><span>$$begin{aligned} f(z_{1},z_{2})^{2}+left( frac{partial f(z_{1},z_{2})}{partial z_{1}}right) ^{2}+g(z_{1},z_{2})^{2}+left( frac{partial g(z_{1},z_{2})}{partial z_{1}}right) ^{2}=1 end{aligned}$$</span></div></div><p>in <span>(mathbb {C}^{2})</span>. In addition, we consider the Bi-Fermat type cubic difference equation </p><div><div><span>$$begin{aligned} f(z)^{3}+g(z)^{3}+f(z+c)^{3}+g(z+c)^{3}=1 end{aligned}$$</span></div></div><p>in <span>(mathbb {C})</span> and obtain partial meromorphic solutions on the above equation.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"14 6","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142645697","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}
引用次数: 0
Value distribution of meromorphic functions concerning differences 关于差分的分形函数的值分布
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-11-16 DOI: 10.1007/s13324-024-00990-3
Zhiying He, Ge Wang, Mingliang Fang
{"title":"Value distribution of meromorphic functions concerning differences","authors":"Zhiying He,&nbsp;Ge Wang,&nbsp;Mingliang Fang","doi":"10.1007/s13324-024-00990-3","DOIUrl":"10.1007/s13324-024-00990-3","url":null,"abstract":"<div><p>In this paper, we study value distribution of meromorphic functions concerning differences and mainly prove the following result: Let <i>f</i> be a transcendental meromorphic function of <span>(1 le rho (f) &lt; infty )</span>, let <i>c</i> be a nonzero constant, <i>n</i> a positive integer, and let <i>P</i>, <i>Q</i> be two polynomials. If <span>(max left{ lambda (f-P), lambda left( frac{1}{f}right) right} &lt;rho (f))</span> and <span>(Delta _{c}^{n}f not equiv 0)</span>, then we have (i) <span>(delta (Q, Delta _c^n f)=0)</span> and <span>(lambda (Delta _{c}^{n}f-Q)=rho (f))</span>, for <span>(Delta _{c}^{n}Pnot equiv Q)</span>; (ii) <span>(delta (Q, Delta _c^n f)=1)</span> and <span>(lambda (Delta _{c}^{n}f-Q)&lt;rho (f))</span>, for <span>(Delta _{c}^{n}Pequiv Q)</span>. The results obtained in this paper extend and improve some results due to Chen-Shon[J Math Anal Appl 2008], [Sci China Ser A 2009], Liu[Rocky Mountain J Math 2011], Cui-Yang[Acta Math Sci Ser B 2013], Chen[Complex Var Elliptic Equ 2013], Wang-Liu-Fang[Acta Math. Sinica (Chinese Ser) 2016].</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"14 6","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142645730","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}
引用次数: 0
Integrable geodesic flow in 3D and webs of maximal rank 三维可积分大地流和最大秩网
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-11-11 DOI: 10.1007/s13324-024-00987-y
Sergey I. Agafonov
{"title":"Integrable geodesic flow in 3D and webs of maximal rank","authors":"Sergey I. Agafonov","doi":"10.1007/s13324-024-00987-y","DOIUrl":"10.1007/s13324-024-00987-y","url":null,"abstract":"<div><p>We characterize geodesic flows, admitting two commuting quadratic integrals with common principal directions, in terms of the geodesic 4-webs such that the tangents to the web leaves are common zero directions of the integrals. We prove that, under some natural geometric hypothesis, the metric is of Stäckel type.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"14 6","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142600559","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}
引用次数: 0
On entire solutions of certain partial differential equations 论某些偏微分方程的全解
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-11-09 DOI: 10.1007/s13324-024-00988-x
Feng Lü, Wenqi Bi
{"title":"On entire solutions of certain partial differential equations","authors":"Feng Lü,&nbsp;Wenqi Bi","doi":"10.1007/s13324-024-00988-x","DOIUrl":"10.1007/s13324-024-00988-x","url":null,"abstract":"<div><p>We firstly describe entire solutions of variation of the well-known PDE of tubular surfaces. In addition, we consider entire solutions of certain partial differential equations, which are related with the Picard’s little theorem. Moreover, we obtain a Tumura-Clunie type theorem in <span>({mathbb {C}}^{m})</span>, which is an improvement of a result given by Hu-Yang (Bull Aust Math Soc 90: 444-456, 2014).</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"14 6","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142598863","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}
引用次数: 0
Multiple nontrivial solutions for a double phase system with concave-convex nonlinearities in subcritical and critical cases 具有凹凸非线性的双相系统在次临界和临界情况下的多个非微妙解
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-11-06 DOI: 10.1007/s13324-024-00985-0
Yizhe Feng, Zhanbing Bai
{"title":"Multiple nontrivial solutions for a double phase system with concave-convex nonlinearities in subcritical and critical cases","authors":"Yizhe Feng,&nbsp;Zhanbing Bai","doi":"10.1007/s13324-024-00985-0","DOIUrl":"10.1007/s13324-024-00985-0","url":null,"abstract":"<div><p>In this article, we study the double phase elliptic system which contain with the parametric concave-convex nonlinearities and critical growth. The introduction of mixed critical terms brings some difficulties to the problem. For example, in proving that the solution is nontrivial, we need to do an additional series of studies on scalar equation. By introducing a new optimal constant <span>(S_{alpha ,beta })</span> in the double phase system, considering the different magnitude relationships of the exponential terms, and using the fibering method in form of the Nehari manifold and the Brezis-Lieb Lemma, the existence and multiplicity of solutions in subcritical and critical cases are obtained separately.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"14 6","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587791","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}
引用次数: 0
Optimal temporal decay rates of solutions for combustion of compressible fluids 可压缩流体燃烧解决方案的最佳时间衰减率
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-11-06 DOI: 10.1007/s13324-024-00984-1
Shengbin Fu, Wenting Huang, Weiwei Wang
{"title":"Optimal temporal decay rates of solutions for combustion of compressible fluids","authors":"Shengbin Fu,&nbsp;Wenting Huang,&nbsp;Weiwei Wang","doi":"10.1007/s13324-024-00984-1","DOIUrl":"10.1007/s13324-024-00984-1","url":null,"abstract":"<div><p>This paper investigates the temporal decay rates of solutions to the Cauchy problem of a model, which describes the combustion of the compressible fluid. Suppose that the initial data is a small perturbation near the equilibrium state <span>((rho _infty , 0,theta _infty ,zeta ))</span>, where <span>(rho _infty &gt;0)</span>, <span>(theta _infty &lt;theta _I)</span> (the ignition temperature), and <span>(0&lt; zeta leqslant 1)</span>, we first establish the global-in-time existence of strong solutions via a standard continuity argument. With the additional <span>(L^1)</span>-integrability of the initial perturbation, we then employ the Fourier theory and the cancellation mechanism of low-medium frequent part to derive the optimal temporal decay rates of all-order derivatives of strong solutions. Our work is a natural continuation of previous result in the case of <span>(theta _infty &gt;theta _I)</span> discussed in Wang and Wen (Sci China Math 65:1199–1228 (2022).</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"14 6","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587790","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}
引用次数: 0
Normalized solutions to HLS upper critical focusing Choquard equation with a non-autonomous nonlocal perturbation 具有非自主非局部扰动的 HLS 上临界聚焦 Choquard 方程的归一化解
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-11-05 DOI: 10.1007/s13324-024-00979-y
Ziheng Zhang, Jianlun Liu, Hong-Rui Sun
{"title":"Normalized solutions to HLS upper critical focusing Choquard equation with a non-autonomous nonlocal perturbation","authors":"Ziheng Zhang,&nbsp;Jianlun Liu,&nbsp;Hong-Rui Sun","doi":"10.1007/s13324-024-00979-y","DOIUrl":"10.1007/s13324-024-00979-y","url":null,"abstract":"<div><p>This paper is concerned with the following HLS upper critical focusing Choquard equation with a non-autonomous nonlocal perturbation </p><div><div><span>$$begin{aligned} {left{ begin{array}{ll} -{Delta }u-mu (I_alpha *[h|u|^p])h|u|^{p-2}u-(I_alpha *|u|^{2^*_alpha })|u|^{2^*_alpha -2}u=lambda u text{ in } mathbb {R}^N, int _{mathbb {R}^N} u^2 dx = c, end{array}right. } end{aligned}$$</span></div></div><p>where <span>(mu ,c&gt;0)</span>, <span>(N ge 3)</span>, <span>(0&lt;alpha &lt;N)</span>, <span>(2_alpha :=frac{N+alpha }{N}&lt;p&lt;2^*_alpha :=frac{N+alpha }{N-2})</span>, <span>(lambda in mathbb {R})</span> is a Lagrange multiplier, <span>(I_alpha )</span> is the Riesz potential and <span>(h:mathbb {R}^Nrightarrow (0,infty ))</span> is a continuous function. Under a class of reasonable assumptions on <i>h</i>, we prove the existence of normalized solutions to the above problem for the case <span>(frac{N+alpha +2}{N}le p&lt;frac{N+alpha }{N-2})</span> and discuss its asymptotical behaviors as <span>(mu rightarrow 0^+)</span> and <span>(crightarrow 0^+)</span> respectively. When <span>(frac{N+alpha }{N}&lt;p&lt;frac{N+alpha +2}{N})</span>, we obtain the existence of one local minimizer after considering a suitable minimization problem.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"14 6","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587740","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}
引用次数: 0
Existence and uniqueness results for a class of obstacle problem via Young’s measure theory 通过杨氏量纲理论求一类障碍问题的存在性和唯一性结果
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-11-02 DOI: 10.1007/s13324-024-00972-5
Mouad Allalou, Mohamed El Ouaarabi, Abderrahmane Raji
{"title":"Existence and uniqueness results for a class of obstacle problem via Young’s measure theory","authors":"Mouad Allalou,&nbsp;Mohamed El Ouaarabi,&nbsp;Abderrahmane Raji","doi":"10.1007/s13324-024-00972-5","DOIUrl":"10.1007/s13324-024-00972-5","url":null,"abstract":"<div><p>The purpose of this article is to prove the existence and uniqueness of weak solutions to the following obstacle problem of <i>p</i>-Laplace-type: </p><div><div><span>$$begin{aligned} displaystyle int _{Omega }sigma _1(z,Du-mathcal {F}(u)):D(v-u)+sigma _2(z,Du):(v-u)+ leftlangle uvert uvert ^{p-2}, v- urightrangle mathrm {~d}zge 0, end{aligned}$$</span></div></div><p>with data belonging to the dual of Sobolev spaces. The main result is demonstrated by means of Kinderlehrer and Stampacchia’s Theorem and Young’s measure theory.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"14 6","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142565978","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}
引用次数: 0
No eigenvectors embedded in the singular continuous spectrum of Schrödinger operators 薛定谔算子奇异连续谱中没有嵌入特征向量
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-10-30 DOI: 10.1007/s13324-024-00948-5
Kota Ujino
{"title":"No eigenvectors embedded in the singular continuous spectrum of Schrödinger operators","authors":"Kota Ujino","doi":"10.1007/s13324-024-00948-5","DOIUrl":"10.1007/s13324-024-00948-5","url":null,"abstract":"<div><p>In general a Schrödinger operator with a sparse potential has singular continuous spectrum, and some open interval is purely singular continuous spectrum. We give a sufficient condition so that the endpoint of the open interval is not an eigenvalue. An example of a Schrödinger operator with a negative sparse potential on the half-line which has no nonnegative embedded eigenvalue for any boundary conditions is given.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"14 6","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142555267","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}
引用次数: 0
Generalized Lipschitz classes in uniform metric and q-Dunkl Fourier transforms 统一度量和 q-Dunkl 傅立叶变换中的广义 Lipschitz 类
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-10-29 DOI: 10.1007/s13324-024-00983-2
Sergey Volosivets
{"title":"Generalized Lipschitz classes in uniform metric and q-Dunkl Fourier transforms","authors":"Sergey Volosivets","doi":"10.1007/s13324-024-00983-2","DOIUrl":"10.1007/s13324-024-00983-2","url":null,"abstract":"<div><p>For a function defined on <span>({mathbb {R}}_q)</span> we define two new variants of a modulus of smoothness and give a Boas type result about connection between the smoothness of this function and the behavior of its q-Dunkle Fourier transform near zero and at infinity.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"14 6","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142524411","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}
引用次数: 0
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