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Electronic Journal of Differential Equations最新文献

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Holder estimates and asymptotic behavior for degenerate elliptic equations in the half space 半空间中退化椭圆方程的Holder估计及其渐近性态
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-04-05 DOI: 10.58997/ejde.2023.33
Xiaobiao Jia, Shan Ma
{"title":"Holder estimates and asymptotic behavior for degenerate elliptic equations in the half space","authors":"Xiaobiao Jia, Shan Ma","doi":"10.58997/ejde.2023.33","DOIUrl":"https://doi.org/10.58997/ejde.2023.33","url":null,"abstract":"In this article we investigate the asymptotic behavior at infinity of viscosity solutions to degenerate elliptic equations. We obtain Holder estimates, up to the flat boundary, by using the rescaling method. Also as a byproduct we obtain a Liouville type result on Baouendi-Grushin type operators.","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45497757","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Pyramidal traveling fronts of a time periodic diffusion equation with degenerate monostable nonlinearity 退化单稳态非线性时间周期扩散方程的金字塔行波
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-04-03 DOI: 10.58997/ejde.2023.31
Z. Bu, Chen-Lu Wang, Xin-Tian Zhang
{"title":"Pyramidal traveling fronts of a time periodic diffusion equation with degenerate monostable nonlinearity","authors":"Z. Bu, Chen-Lu Wang, Xin-Tian Zhang","doi":"10.58997/ejde.2023.31","DOIUrl":"https://doi.org/10.58997/ejde.2023.31","url":null,"abstract":"This article focuses on the nonplanar traveling fronts of degenerate monostable time periodic reaction-diffusion equations in Rn with n≥3. By constructing a couple of proper supersolution and subsolution, we prove the existence of periodic pyramidal traveling front in R3 and then in Rn with n>3.","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43121625","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
A weighted (p,2)-equation with double resonance 具有双重共振的加权(p,2)方程
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-03-30 DOI: 10.58997/ejde.2023.30
Zhenhai Liu, Nikolaos S. Papageorgiou
{"title":"A weighted (p,2)-equation with double resonance","authors":"Zhenhai Liu, Nikolaos S. Papageorgiou","doi":"10.58997/ejde.2023.30","DOIUrl":"https://doi.org/10.58997/ejde.2023.30","url":null,"abstract":"We consider a Dirichlet problem driven by a weighted (p,2)-Laplacian with a reaction which is resonant both at (pminfty) and at zero (double resonance). We prove a multiplicity theorem producing three nontrivial  smooth solutions with sign information and ordered. In the appendix we develop the spectral properties of the weighted r-Laplace differential operator.","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42095355","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 1
Friedrichs extension of singular symmetric differential operators 奇异对称微分算子的Friedrichs推广
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-03-27 DOI: 10.58997/ejde.sp.02.b1
Qinglan Bao, Guangsheng Wei, A. Zettl
{"title":"Friedrichs extension of singular symmetric differential operators","authors":"Qinglan Bao, Guangsheng Wei, A. Zettl","doi":"10.58997/ejde.sp.02.b1","DOIUrl":"https://doi.org/10.58997/ejde.sp.02.b1","url":null,"abstract":"For singular even order symmetric differential operators we find the matrices which determine all symmetric extensions of the minimal operator. And for each of these symmetric operators which is bounded below we find the boundary condition of its Friedrichs extension. The operators of regular problems are bounded below and thus each one has a symmetric extension and thus its symmetric extension has a Friedrichs extension.\u0000See also https://ejde.math.txstate.edu/special/02/b1/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44382564","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Regular solutions to elliptic equations 椭圆方程的正则解
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-03-27 DOI: 10.58997/ejde.sp.02.c2
A. Castro, Jon Jacobsen
{"title":"Regular solutions to elliptic equations","authors":"A. Castro, Jon Jacobsen","doi":"10.58997/ejde.sp.02.c2","DOIUrl":"https://doi.org/10.58997/ejde.sp.02.c2","url":null,"abstract":"A review of results and techniques on the existence of regular radial solutions to second order elliptic boundary value problems driven by  linear and quasilinear operators is presented. Of particular interest are results where the solvability of a given  elliptic problem can be analyzed by the relationship between the  spectrum of the operator and the behavior of the nonlinearity near infinity and at zero.  Energy arguments and Pohozaev type identities are used extensively in that analysis. An appendix with a proof of the contraction mapping  principle best suited for using continuous dependence to ordinary  differential equations on initial conditions is presented. Another appendix on the phase plane analysis as needed to take advantage  of initial conditions is also included. For studies on singular solutions  the reader is referred to Ardila et al., Milan J. Math (2014)  and references therein.\u0000See also https://ejde.math.txstate.edu/special/02/c2/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41937642","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Nonlocal advection diffusion equations and the two-slit experiment in quantum mechanics 量子力学中的非局部平流扩散方程与双缝实验
4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-03-27 DOI: 10.58997/ejde.sp.02.w1
Glenn Webb
{"title":"Nonlocal advection diffusion equations and the two-slit experiment in quantum mechanics","authors":"Glenn Webb","doi":"10.58997/ejde.sp.02.w1","DOIUrl":"https://doi.org/10.58997/ejde.sp.02.w1","url":null,"abstract":"We analyze a partial differential equation that models the two-slit experiment of quantum mechanics. The state variable of the equation is the probability density function of particle positions. The equation has a diffusion term corresponding to the random movement of particles, and a nonlocal advection term corresponding to the movement of particles in the transverse directionperpendicular to their forward movement. The model is compared to the Schrodinger equation model of the experiment. The model supports the ensemble interpretation of quantum mechanics.
 See also https://ejde.math.txstate.edu/special/02/w1/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135891565","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Resonant solutions for elliptic systems with Neumann boundary conditions 具有Neumann边界条件的椭圆系统的共振解
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-03-27 DOI: 10.58997/ejde.sp.02.d1
B. B. Delgado, R. Pardo
{"title":"Resonant solutions for elliptic systems with Neumann boundary conditions","authors":"B. B. Delgado, R. Pardo","doi":"10.58997/ejde.sp.02.d1","DOIUrl":"https://doi.org/10.58997/ejde.sp.02.d1","url":null,"abstract":"We consider a sublinear perturbation of an elliptic eigenvalue system with homogeneous Neumann boundary conditions. For oscillatory nonlinearities and using bifurcation from infinity, we prove the existence of an unbounded sequence of turning points and an unbounded sequence of resonant solutions. \u0000See also https://ejde.math.txstate.edu/special/02/d1/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43674256","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Positive solutions for nonlinear fractional Laplacian problems 非线性分数阶拉普拉斯问题的正解
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-03-27 DOI: 10.58997/ejde.sp.02.h1
Elliott Hollifield
{"title":"Positive solutions for nonlinear fractional Laplacian problems","authors":"Elliott Hollifield","doi":"10.58997/ejde.sp.02.h1","DOIUrl":"https://doi.org/10.58997/ejde.sp.02.h1","url":null,"abstract":"We consider a class of nonlinear fractional Laplacian problems satisfying the homogeneous Dirichlet condition on the exterior of a bounded domain. We prove the existence of a positive weak solution for classes of nonlinearities which are either sublinear or asymptotically linear at infinity. We use the method of sub-and-supersolutions to establish the results. We also provide numerical bifurcation diagrams, corresponding to the theoretical results, using the finite element method in one  dimension.\u0000See also https://ejde.math.txstate.edu/special/02/h1/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43652336","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Determining the background driving process of the Ornstein-Uhlenbeck model 确定Ornstein-Uhlenbeck模型的背景驱动过程
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-03-27 DOI: 10.58997/ejde.sp.02.m1
M. Mariani, Peter K. Asante, William Kubin, Osei K. Tweneboah, Maria P. Beccar-Varela
{"title":"Determining the background driving process of the Ornstein-Uhlenbeck model","authors":"M. Mariani, Peter K. Asante, William Kubin, Osei K. Tweneboah, Maria P. Beccar-Varela","doi":"10.58997/ejde.sp.02.m1","DOIUrl":"https://doi.org/10.58997/ejde.sp.02.m1","url":null,"abstract":"In this work, we determine appropriate background driving processes for the 3-component superposed Ornstein-Uhlenbeck model by analyzing the fractal characteristics of the data sets using the rescaled range analysis (R/S), the detrended fluctuation analysis (DFA), and the diffusion entropy analysis (DEA). \u0000See also https://ejde.math.txstate.edu/special/02/m1/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44676998","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Local min-orthogonal principle and its applications for solving multiple solution problems 局部最小正交原理及其在求解多解问题中的应用
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-03-27 DOI: 10.58997/ejde.sp.02.l1
Meiqin Li, Jianxin Zhou
{"title":"Local min-orthogonal principle and its applications for solving multiple solution problems","authors":"Meiqin Li, Jianxin Zhou","doi":"10.58997/ejde.sp.02.l1","DOIUrl":"https://doi.org/10.58997/ejde.sp.02.l1","url":null,"abstract":"In this article we establish a double-orthogonal principle, and a local min-orthogonal method with its step size rule, and its convergence under assumptions more general than those in its previous versions. With such a general framework, we justify mathematically the two new  algorithms proposed for solving W-type problems. Numerical examples for finding multiple solutions to W-type and to mixed M-W-type problems illustrate the flexibility of this method. \u0000See also","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46132387","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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