{"title":"Strong convergence in Bopp-Podolsky-Proca type constructions","authors":"Emmanuel Hebey","doi":"10.3934/dcds.2023013","DOIUrl":"https://doi.org/10.3934/dcds.2023013","url":null,"abstract":"","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88568088","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":"Radially symmetric stationary solutions for certain chemotaxis systems in higher dimensions: A geometric approach","authors":"Yutaka Ichida","doi":"10.3934/dcds.2022188","DOIUrl":"https://doi.org/10.3934/dcds.2022188","url":null,"abstract":"","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75458327","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":"Modified scattering for the nonlinear nonlocal Schrödinger equation in two space dimensions","authors":"N. Hayashi, P. Naumkin","doi":"10.3934/dcds.2023065","DOIUrl":"https://doi.org/10.3934/dcds.2023065","url":null,"abstract":"","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79264726","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":"Vacuum and singularity formation for compressible Euler equations with time-dependent damping","authors":"Ying Sui, Weiqiang Wang, Huimin Yu","doi":"10.3934/dcds.2022184","DOIUrl":"https://doi.org/10.3934/dcds.2022184","url":null,"abstract":"In this paper, vacuum and singularity formation are considered for compressible Euler equations with time-dependent damping. For $ 1<gamma{leq} 3 $, by constructing some new control functions ingeniously, we obtain the lower bounds estimates on density for arbitrary classical solutions. Basing on these lower estimates, we succeed in proving the singular formation theorem for all $ lambda $, which was open in [19] for some cases. Moreover, the singularity formation of the compressible Euler equations when $ gamma = 3 $ is investigated, too.","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134996609","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":"Refined spike profiles of constraint minimizers for the planar Schrödinger-Poisson system with logarithmic potentials","authors":"Yujin Guo, Wenning Liang, Yan Li","doi":"10.3934/dcds.2023100","DOIUrl":"https://doi.org/10.3934/dcds.2023100","url":null,"abstract":"","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74986822","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":"Random Gibbs $ u $-state for partially hyperbolic on fibers system","authors":"Xue Liu","doi":"10.3934/dcds.2023070","DOIUrl":"https://doi.org/10.3934/dcds.2023070","url":null,"abstract":"","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73935100","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":"Spatial dynamics of a nonlocal dispersal Leslie-Gower predator-prey model with some shifting habitats","authors":"Qinhe Fang, Hongmei Cheng, Rong Yuan","doi":"10.3934/dcds.2023037","DOIUrl":"https://doi.org/10.3934/dcds.2023037","url":null,"abstract":"","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76720267","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}
We are concerned with the quasi-periodic semilinear Duffing equation $ x''+omega^2x+g(x,t) = 0, $ where $ omega $ is a Diophantine number, $ g(x,t) $ is bounded, real analytic in $ x $ and $ t $, and is quasi-periodic in $ t $ with the frequency $ tilde{omega} = (1, alpha) $, where $ alpha $ is Liouvillean. Without assuming the twist condition and the polynomial-like condition on this equation, we will prove the boundedness of all solutions.
我们关注拟周期半线性Duffing方程$ x''+omega^2x+g(x,t) = 0, $，其中$ omega $是丢芬图数，$ g(x,t) $是有界的，在$ x $和$ t $是实解析的，在$ t $是拟周期的，频率为$ tilde{omega} = (1, alpha) $，其中$ alpha $是Liouvillean。在不假设该方程的扭转条件和类多项式条件的情况下，证明了所有解的有界性。
{"title":"Boundedness of semilinear Duffing equations with Liouvillean frequency","authors":"Min Li, Xiong Li","doi":"10.3934/dcds.2023127","DOIUrl":"https://doi.org/10.3934/dcds.2023127","url":null,"abstract":"We are concerned with the quasi-periodic semilinear Duffing equation $ x''+omega^2x+g(x,t) = 0, $ where $ omega $ is a Diophantine number, $ g(x,t) $ is bounded, real analytic in $ x $ and $ t $, and is quasi-periodic in $ t $ with the frequency $ tilde{omega} = (1, alpha) $, where $ alpha $ is Liouvillean. Without assuming the twist condition and the polynomial-like condition on this equation, we will prove the boundedness of all solutions.","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135319485","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}
In this paper we prove a Liouville theorem for the Chern–Simons–Schrödinger equation. This result is consistent with the soliton resolution conjecture for initial data that does not lie in a weighted space. See [10] for the soliton resolution result in a weighted space.
{"title":"A Liouville theorem for the Chern–Simons–Schrödinger equation","authors":"Benjamin Dodson","doi":"10.3934/dcds.2023110","DOIUrl":"https://doi.org/10.3934/dcds.2023110","url":null,"abstract":"In this paper we prove a Liouville theorem for the Chern–Simons–Schrödinger equation. This result is consistent with the soliton resolution conjecture for initial data that does not lie in a weighted space. See [10] for the soliton resolution result in a weighted space.","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135839031","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}
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