{"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":null,"pages":null},"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}
{"title":"On entire solutions of certain partial differential equations","authors":"Feng Lü, 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":null,"pages":null},"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}
{"title":"Multiple nontrivial solutions for a double phase system with concave-convex nonlinearities in subcritical and critical cases","authors":"Yizhe Feng, 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":null,"pages":null},"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}
{"title":"Optimal temporal decay rates of solutions for combustion of compressible fluids","authors":"Shengbin Fu, Wenting Huang, 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 >0)</span>, <span>(theta _infty <theta _I)</span> (the ignition temperature), and <span>(0< 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 >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":null,"pages":null},"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}
{"title":"Normalized solutions to HLS upper critical focusing Choquard equation with a non-autonomous nonlocal perturbation","authors":"Ziheng Zhang, Jianlun Liu, 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>0)</span>, <span>(N ge 3)</span>, <span>(0<alpha <N)</span>, <span>(2_alpha :=frac{N+alpha }{N}<p<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<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}<p<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":null,"pages":null},"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}
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, Mohamed El Ouaarabi, 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":null,"pages":null},"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}
{"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":null,"pages":null},"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}
{"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":null,"pages":null},"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}
{"title":"Decoupling of modes for low regularity hyperbolic systems","authors":"Hart F. Smith","doi":"10.1007/s13324-024-00982-3","DOIUrl":"10.1007/s13324-024-00982-3","url":null,"abstract":"<div><p>We show that the coupling operator between distinct modes of a second-order hyperbolic system is smoothing of degree one, where we assume that the eigenvalues of the symbol are of constant rank, and that the coefficients of the system have bounded derivatives of second order. An important example is the wave equation for linear isotropic elasticity, where our assumption states that the Lamé parameters and mass density have bounded derivatives of second order. This extends a result for the elastic wave equation established by Brytik, et.al.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142518987","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}
Manuel D. Contreras, Francisco J. Cruz-Zamorano, Maria Kourou, Luis Rodríguez-Piazza
{"title":"On the Hardy number of Koenigs domains","authors":"Manuel D. Contreras, Francisco J. Cruz-Zamorano, Maria Kourou, Luis Rodríguez-Piazza","doi":"10.1007/s13324-024-00981-4","DOIUrl":"10.1007/s13324-024-00981-4","url":null,"abstract":"<div><p>This work studies the Hardy number of hyperbolic planar domains satisfying Abel’s inclusion property, which are usually known as Koenigs domains. More explicitly, we prove that the Hardy number of a Koenings domains whose complement is non-polar is greater than or equal to 1/2, and this lower bound is sharp. In contrast to this result, we provide examples of general domains whose Hardy numbers are arbitrarily small. Additionally, we outline the connection of the aforementioned class of domains with the discrete dynamics of the unit disc and obtain results on the range of Hardy number of Koenigs maps, in the hyperbolic and parabolic case.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13324-024-00981-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142518427","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}