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A remark for spatial analyticity around straining flows 关于应变流动的空间分析的评述
Differential Equations and Applications Pub Date : 2018-01-01 DOI: 10.7153/DEA-2018-10-26
S. Hattori, O. Sawada
{"title":"A remark for spatial analyticity around straining flows","authors":"S. Hattori, O. Sawada","doi":"10.7153/DEA-2018-10-26","DOIUrl":"https://doi.org/10.7153/DEA-2018-10-26","url":null,"abstract":"Time-local existence of unique smooth solutions to the Navier-Stokes equations in the whole space with linearly growing initial data has been established, via smoothing properties of Ornstein-Uhlenbeck semigroup. It has also been shown that the solution is real-analytic in spatial variables around rotating flows. This note is devoted to prove the spatial analyticity for cases of straining flows and shear flows. It is estimated the size of radius of convergence of Taylor series, due to estimates for higher order derivatives and Cauchy-Hadamard theorem.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"54 1","pages":"387-395"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75095166","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}
引用次数: 0
Lyapunov inequalities for two-parametric quantum Hamiltonian systems and their applications 双参数量子哈密顿系统的Lyapunov不等式及其应用
Differential Equations and Applications Pub Date : 2018-01-01 DOI: 10.7153/DEA-2018-10-19
Yousef Gholami
{"title":"Lyapunov inequalities for two-parametric quantum Hamiltonian systems and their applications","authors":"Yousef Gholami","doi":"10.7153/DEA-2018-10-19","DOIUrl":"https://doi.org/10.7153/DEA-2018-10-19","url":null,"abstract":"This paper deals with study of the two-parametric quantum Hamiltonian systems. The main objective in our study is Lyapunov inequalities of the two-parametric quantum Hamiltonian systems. In this paper, we first define two-parametric quantum analogous of the Leibniz rule, Cauchy-Schwarz and Holder inequalities and consequently as theoretical part of our main results, by the use of new Leibniz rule and Cauchy-Schwarz inequality on the considered Hamiltonian systems we obtain corresponding Lyapunov inequalities. Applicability of the obtained Lyapunov inequalities is examined by presenting a disconjugacy and at the same time a nonexistence criterion for the related Hamiltonian systems.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"24 1","pages":"261-276"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88105250","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}
引用次数: 1
On Instability of Steady–State Three–Dimensional Flows of an Ideal Compressible Fluid 理想可压缩流体稳态三维流动的不稳定性
Differential Equations and Applications Pub Date : 2018-01-01 DOI: 10.12691/IJPDEA-5-1-2
Y. Gubarev
{"title":"On Instability of Steady–State Three–Dimensional Flows of an Ideal Compressible Fluid","authors":"Y. Gubarev","doi":"10.12691/IJPDEA-5-1-2","DOIUrl":"https://doi.org/10.12691/IJPDEA-5-1-2","url":null,"abstract":"The problem on linear stability of stationary spatial flows of an inviscid compressible fluid entirely occupying a certain volume with quiescent solid impenetrable boundary in absence of external mass forces is studied. Applying the direct Lyapunov method, such flows are proved to be absolutely unstable under small three–dimensional (3D) perturbations. Constructive conditions for linear practical instability are obtained. The a priori exponential lower estimate for the growth of the considered perturbations in time is found.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"103 1","pages":"10-18"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80723230","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}
引用次数: 0
Existence and multiplicity solutions for a nonlocal equation of Kirchhoff type 一类Kirchhoff型非局部方程的存在性解和多重解
Differential Equations and Applications Pub Date : 2018-01-01 DOI: 10.7153/dea-2018-10-25
Lin Li, Jijiang Sun
{"title":"Existence and multiplicity solutions for a nonlocal equation of Kirchhoff type","authors":"Lin Li, Jijiang Sun","doi":"10.7153/dea-2018-10-25","DOIUrl":"https://doi.org/10.7153/dea-2018-10-25","url":null,"abstract":"","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"138 1","pages":"369-386"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74551839","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}
引用次数: 3
Periodic solutions for nonlinear fractional differential systems 非线性分数阶微分系统的周期解
Differential Equations and Applications Pub Date : 2018-01-01 DOI: 10.7153/DEA-2018-10-21
S. Abbas, M. Benchohra, S. Bouriah, J. Nieto
{"title":"Periodic solutions for nonlinear fractional differential systems","authors":"S. Abbas, M. Benchohra, S. Bouriah, J. Nieto","doi":"10.7153/DEA-2018-10-21","DOIUrl":"https://doi.org/10.7153/DEA-2018-10-21","url":null,"abstract":"In this paper, we establish some existence and uniqueness results for periodic solutions for a class of fractional differential equations with the Caputo fractional derivative. The arguments are based upon the Banach contraction principle, and Schaefer’s fixed point theorem.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"52 1","pages":"299-316"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74869333","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}
引用次数: 3
Factorization techniques for the nonlinear model of quasi-stationary processes in crystalline semiconductors 晶体半导体中准平稳过程非线性模型的因子分解技术
Differential Equations and Applications Pub Date : 2018-01-01 DOI: 10.7153/DEA-2018-10-24
B. Juárez-Campos, E. Kaikina, P. Naumkin, H. R. Paredes
{"title":"Factorization techniques for the nonlinear model of quasi-stationary processes in crystalline semiconductors","authors":"B. Juárez-Campos, E. Kaikina, P. Naumkin, H. R. Paredes","doi":"10.7153/DEA-2018-10-24","DOIUrl":"https://doi.org/10.7153/DEA-2018-10-24","url":null,"abstract":"We consider the question of global existence and asymptotics of small solutions of a certain pseudoparabolic equation in one dimension . This model is motivated by the wave equation for media with a strong spatial dispersion, which appear in the nonlinear theory of the quasi-stationary processes in the electric media. We develop the factorization technique to study the large time asymptotics of solutions.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"52 1","pages":"341-367"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90672289","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}
引用次数: 0
Box-counting dimension of oscillatory solutions to the Emden-Fowler equation Emden-Fowler方程振荡解的盒计数维数
Differential Equations and Applications Pub Date : 2018-01-01 DOI: 10.7153/DEA-2018-10-17
Takanao Kanemitsu, Satoshi Tanaka
{"title":"Box-counting dimension of oscillatory solutions to the Emden-Fowler equation","authors":"Takanao Kanemitsu, Satoshi Tanaka","doi":"10.7153/DEA-2018-10-17","DOIUrl":"https://doi.org/10.7153/DEA-2018-10-17","url":null,"abstract":"The box-counting dimension of graphs of oscillatory solutions to the Emden-Fowler equation is studied. The half-linear equation is also considered. Mathematics subject classification (2010): 34C10, 28A80.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"252 1","pages":"239-250"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77643463","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}
引用次数: 2
Nonlocal boundary value problems for (p, q)-difference equations (p, q)差分方程的非局部边值问题
Differential Equations and Applications Pub Date : 2018-01-01 DOI: 10.7153/DEA-2018-10-11
Nattapong Kamsrisuk, C. Promsakon, S. Ntouyas, J. Tariboon
{"title":"Nonlocal boundary value problems for (p, q)-difference equations","authors":"Nattapong Kamsrisuk, C. Promsakon, S. Ntouyas, J. Tariboon","doi":"10.7153/DEA-2018-10-11","DOIUrl":"https://doi.org/10.7153/DEA-2018-10-11","url":null,"abstract":"In this paper we study existence and uniqueness of solutions for a boundary value problem for (p,q) -difference equations with nonlocal integral boundary conditions, by using classical fixed point theorems. Examples illustrating the main results are also presented. Mathematics subject classification (2010): 05A30, 39A13, 34A12.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"71 1","pages":"183-195"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82122630","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}
引用次数: 13
Uniform exponential stability in the sense of Hyers and Ulam for periodic time varying linear systems 周期时变线性系统Hyers和Ulam意义上的一致指数稳定性
Differential Equations and Applications Pub Date : 2018-01-01 DOI: 10.7153/DEA-2018-10-15
Bakht Zada
{"title":"Uniform exponential stability in the sense of Hyers and Ulam for periodic time varying linear systems","authors":"Bakht Zada","doi":"10.7153/DEA-2018-10-15","DOIUrl":"https://doi.org/10.7153/DEA-2018-10-15","url":null,"abstract":"We prove that the uniform exponential stability of time depended p -periodic system Ψ̇(t) = Π(t)Ψ(t), t ∈ R+, Ψ(t) ∈ Cn is equivalent to its Hyers–Ulam stability. As a tool, we consider the exact solution of the Cauchy problem { Θ̇(t) = Π(t)Θ(t)+ eiαtζ (t), t ∈ R+ Θ(0) = Θ0 as the approximate solution of Ψ̇(t) = Π(t)Ψ(t), t ∈ R+, Ψ(t)∈ Cn , where α is any real number, ζ (t) with ζ (0) = 0 , is a p -periodic bounded function on the Banach space S (R+,C) . More precisely we prove that the system Ψ̇(t) = Π(t)Ψ(t), t ∈ R+, Ψ(t) ∈ Cn is Hyers–Ulam stable if and only if it is exponentially stable. We argue that Hyers-Ulam stability concept is quite significant in realistic problems in numerical analysis and economics.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"17 1","pages":"227-234"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87179674","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}
引用次数: 7
Dedicated to memory of Professor ROBERT JANIN 谨以此纪念罗伯特·贾宁教授
Differential Equations and Applications Pub Date : 2018-01-01 DOI: 10.7153/dea-2018-10-01
J. Rakotoson
{"title":"Dedicated to memory of Professor ROBERT JANIN","authors":"J. Rakotoson","doi":"10.7153/dea-2018-10-01","DOIUrl":"https://doi.org/10.7153/dea-2018-10-01","url":null,"abstract":"Professor Robert JANIN was a former teacher in Poitiers (1988-1998); he died in October 2016. His speciality was Optimization Theory and Theory of Control. He obtained his thesis in 1974, at the University of PARIS VI, under the supervision of Professor Pallu de la Barrière. Then, he was hired as a researcher IRIA (nowadays INRIA) where he stayed there from 1967 to 1972 and then was appointed as a researcher at C.N.R.S. (National Center for Scientific Research in France) from 1972 to 1979. During that period, he spent two years (1976-1978) in Africa, in Togo more precisely. He applied to a full professorship position at University CUAG (Centre Universitaire AntillesGuyane) in 1979, where he spent nine years before pursuing his career","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"38 1","pages":"1-2"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84224659","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}
引用次数: 0
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