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Differential Equations and Applications最新文献

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Square mean almost automorphic solution of stochastic evolution equations with impulses on time scales 时间尺度上脉冲随机演化方程的均方根几乎自同构解
Differential Equations and Applications Pub Date : 2018-01-01 DOI: 10.7153/DEA-2018-10-30
Soniya Dhama, Syed Abbas
{"title":"Square mean almost automorphic solution of stochastic evolution equations with impulses on time scales","authors":"Soniya Dhama, Syed Abbas","doi":"10.7153/DEA-2018-10-30","DOIUrl":"https://doi.org/10.7153/DEA-2018-10-30","url":null,"abstract":"In this paper, we study the existence, uniqueness and exponential stability of the square-mean almost automorphic solution for stochastic evolution equation with impulses on time scales. For this purpose, we introduce the concept of equipotentially square-mean almost automorphic sequence and square-mean almost automorphic functions with impulses on time scales. At the end, a numerical example is given to illustrate the effectiveness of the obtained theoretical results.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"12 1","pages":"449-469"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86854813","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: 8
Existence of positive solutions for nonlinear fractional Neumann elliptic equations 非线性分数阶Neumann椭圆方程正解的存在性
Differential Equations and Applications Pub Date : 2018-01-01 DOI: 10.7153/DEA-2018-10-07
Haoqi Ni, Aliang Xia, Xiongjun Zheng
{"title":"Existence of positive solutions for nonlinear fractional Neumann elliptic equations","authors":"Haoqi Ni, Aliang Xia, Xiongjun Zheng","doi":"10.7153/DEA-2018-10-07","DOIUrl":"https://doi.org/10.7153/DEA-2018-10-07","url":null,"abstract":"This article is devoted to study the fractional Neumann elliptic problem ⎧⎪⎨ ⎪⎩ ε2s(−Δ)su+u = up in Ω, ∂νu = 0 on ∂Ω, u > 0 in Ω, where Ω is a smooth bounded domain of RN , N > 2s , 0 < s s0 < 1 , 1 < p < (N +2s)/(N− 2s) , ε > 0 and ν is the outer normal to ∂Ω . We show that there exists at least one nonconstant solution uε to this problem provided ε is small. Moreover, we prove that uε ∈ L∞(Ω) by using Moser-Nash iteration.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"26 1","pages":"115-129"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89380038","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
On a hinged plate equation of nonconstant thickness 关于铰链板的非定厚方程
Differential Equations and Applications Pub Date : 2018-01-01 DOI: 10.7153/DEA-2018-10-16
C. Danet
{"title":"On a hinged plate equation of nonconstant thickness","authors":"C. Danet","doi":"10.7153/DEA-2018-10-16","DOIUrl":"https://doi.org/10.7153/DEA-2018-10-16","url":null,"abstract":"This note is concerned with the problem of existence and uniqueness of solutions for a fourth order boundary value problem that models the deflection of a hinged plate of nonconstant thickness.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"177 1","pages":"235-238"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86225567","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
Existence and uniqueness of monotone positive solutions for a third-order three-point boundary value problem 一类三阶三点边值问题单调正解的存在唯一性
Differential Equations and Applications Pub Date : 2018-01-01 DOI: 10.7153/DEA-2018-10-18
A. Palamides, N. Stavrakakis
{"title":"Existence and uniqueness of monotone positive solutions for a third-order three-point boundary value problem","authors":"A. Palamides, N. Stavrakakis","doi":"10.7153/DEA-2018-10-18","DOIUrl":"https://doi.org/10.7153/DEA-2018-10-18","url":null,"abstract":"In this work we study a third-order three-point boundary-value problem (BVP). We derive sucient conditions that guarantee the positivity of the solution of the corresponding linear BVP Then, based on the classi- cal Guo-Krasnosel'skii's fixed point theorem, we obtain positive solutions to the nonlinear BVP. Additional hypotheses guarantee the uniqueness of the solution.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"33 1","pages":"251-260"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88620767","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: 5
On boundary value problem for equations with cubic nonlinearity and step-wise coefficient 三次非线性阶跃系数方程的边值问题
Differential Equations and Applications Pub Date : 2018-01-01 DOI: 10.7153/dea-2018-10-29
A. Kirichuka, F. Sadyrbaev
{"title":"On boundary value problem for equations with cubic nonlinearity and step-wise coefficient","authors":"A. Kirichuka, F. Sadyrbaev","doi":"10.7153/dea-2018-10-29","DOIUrl":"https://doi.org/10.7153/dea-2018-10-29","url":null,"abstract":"The differential equation with cubic nonlinearity x′′ = −ax + bx3 is considered together with the boundary conditions x(−1) = x(1) = 0 . In the autonomous case, b = const > 0 , the exact number of solutions for the boundary value problem is given. For nonautonomous case, where b = β(t) is a step-wise function, the existence of additional solutions is detected. The reasons for such behaviour are revealed. The example considered in this paper is supplemented by a number of visualizations.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"91 1 1","pages":"433-447"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86466915","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
Properties of solutions of the scalar Riccati equation with complex coefficients and some their applications 复系数标量Riccati方程解的性质及其应用
Differential Equations and Applications Pub Date : 2018-01-01 DOI: 10.7153/DEA-2018-10-20
G. Grigorian
{"title":"Properties of solutions of the scalar Riccati equation with complex coefficients and some their applications","authors":"G. Grigorian","doi":"10.7153/DEA-2018-10-20","DOIUrl":"https://doi.org/10.7153/DEA-2018-10-20","url":null,"abstract":"The definition of normal and extremal solutions of the scalar Riccati equation with complex coefficients is given. Some properties of normal and extremal solutions to Riccati equation are studied. On the basis of the obtained, some theorems which describe the asymptotic behavior of solutions of the system of two linear first order ordinary differential equations are proved (in particular a minimality theorem of a solution of the system of two linear first order ordinary differential equations is proved).","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"60 1","pages":"277-298"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90455730","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
Existence theory for nonlinear Sturm-Liouville problems with non-local boundary conditions 具有非局部边界条件的非线性Sturm-Liouville问题的存在性理论
Differential Equations and Applications Pub Date : 2018-01-01 DOI: 10.7153/DEA-2018-10-09
D. Maroncelli, Jesús F. Rodríguez
{"title":"Existence theory for nonlinear Sturm-Liouville problems with non-local boundary conditions","authors":"D. Maroncelli, Jesús F. Rodríguez","doi":"10.7153/DEA-2018-10-09","DOIUrl":"https://doi.org/10.7153/DEA-2018-10-09","url":null,"abstract":"In this work we provide conditions for the existence of solutions to nonlinear SturmLiouville problems of the form (p(t)x′(t))′ +q(t)x(t)+λx(t) = f (x(t)) subject to non-local boundary conditions ax(0)+bx′(0) = η1(x) and cx(1)+dx′(1) = η2(x). Our approach will be topological, utilizing Schaefer’s fixed point theorem and the LyapunovSchmidt procedure.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"11 1","pages":"147-161"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88614180","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
On grand and small Lebesgue and Sobolev spaces and some applications to PDE's 论大小Lebesgue和Sobolev空间及其在PDE中的应用
Differential Equations and Applications Pub Date : 2018-01-01 DOI: 10.7153/DEA-2018-10-03
A. Fiorenza, M. R. Formica, Amiran Gogatishvili
{"title":"On grand and small Lebesgue and Sobolev spaces and some applications to PDE's","authors":"A. Fiorenza, M. R. Formica, Amiran Gogatishvili","doi":"10.7153/DEA-2018-10-03","DOIUrl":"https://doi.org/10.7153/DEA-2018-10-03","url":null,"abstract":"This paper is essentially a survey on grand and small Lebesgue spaces, which are rearrangement-invariant Banach function spaces of interest not only from the point of view of Function Spaces theory, but also from the point of view of their applications: the corresponding Sobolev spaces are of interest, for instance, in the theory of PDEs. We discuss results of existence, uniqueness and regularity of certain Dirichlet problems, where the knowledge of these spaces plays a central role. The novelty of this paper relies in an unified treatment containing a number of equivalent quasinorms, all written making explicit the dependence of |Ω| , in the discussion of the sharpness of Hölder’s inequality, and in the connection of the results in PDEs with some existing literature. 1. Grand and small Lebesgue spaces: a short overview 1.1. The original motivation Let Ω ⊂ Rn be a bounded domain and f : Ω →Rn , f = ( f 1, ..., f n) be a mapping of Sobolev class W 1,n loc (Ω,R n) . Let us denote by Df (x) : Rn → Rn the differential and by J(x, f ) = detD f (x) the Jacobian of f . After the elementary remark that by Hölder’s inequality the Jacobian J(x, f ) is in Lloc(Ω) , the first fundamental result on the integrability of the Jacobian was due to Müller ([135]): f ∈W (Ω,R), J(x, f ) 0 a.e. ⇒ J(x, f ) ∈ L logLloc(Ω). Mathematics subject classification (2010): 46E30, 35J65.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"27 1","pages":"21-46"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78327821","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: 59
On linear and nonlinear fractional Hadamard boundary value problems 线性和非线性分数阶Hadamard边值问题
Differential Equations and Applications Pub Date : 2018-01-01 DOI: 10.7153/DEA-2018-10-23
Sougata Dhar
{"title":"On linear and nonlinear fractional Hadamard boundary value problems","authors":"Sougata Dhar","doi":"10.7153/DEA-2018-10-23","DOIUrl":"https://doi.org/10.7153/DEA-2018-10-23","url":null,"abstract":"We establish new Lyapunov-type inequalities for linear Hadamard fractional differential equations with pointwise boundary conditions. Furthermore, we employ the contraction mapping principle to obtain the criterion of the existence of a unique solution for a nonlinear fractional Hadamard type boundary value problem.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"10 1","pages":"329-339"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78908933","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
Vanishing magnetic field limits of solutions to the pressureless magnetogasdynamics 无压磁气动力学解的消失磁场极限
Differential Equations and Applications Pub Date : 2018-01-01 DOI: 10.7153/dea-2018-10-10
Hongjun Cheng, Zhongshun Sun
{"title":"Vanishing magnetic field limits of solutions to the pressureless magnetogasdynamics","authors":"Hongjun Cheng, Zhongshun Sun","doi":"10.7153/dea-2018-10-10","DOIUrl":"https://doi.org/10.7153/dea-2018-10-10","url":null,"abstract":"We are interested in the system of conservation laws modeling the pressureless magnetogasdynamics. Firstly, we solve the Riemann problem and obtain five kinds of structures consisting of combinations of shocks, rarefaction waves and contact discontinuities. Secondly, we study the vanishing magnetic field limits of the Riemann solutions to the pressureless magnetogasdynamics and show that the density and velocity in the Riemann solutions to the pressureless magnetogasdynamics converge to the Riemann solutions to the pressureless gas dynamics. The formation processes of delta-shocks and vacuum states are discussed in details.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"396 1","pages":"163-182"},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74945722","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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