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Electronic Journal of Differential Equations最新文献

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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":"31 1","pages":"0"},"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
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":" ","pages":""},"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":" ","pages":""},"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
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":" ","pages":""},"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":" ","pages":""},"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":" ","pages":""},"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
Fucik spectrum with weights and existence of solutions for nonlinear elliptic equations with nonlinear boundary conditions 非线性边界条件下非线性椭圆型方程的Fucik谱及其解的存在性
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-03-27 DOI: 10.58997/ejde.sp.02.m2
N. Mavinga, Q. Morris, S. Robinson
{"title":"Fucik spectrum with weights and existence of solutions for nonlinear elliptic equations with nonlinear boundary conditions","authors":"N. Mavinga, Q. Morris, S. Robinson","doi":"10.58997/ejde.sp.02.m2","DOIUrl":"https://doi.org/10.58997/ejde.sp.02.m2","url":null,"abstract":"We consider the boundary value problem $$displaylines{ - Delta u + c(x) u = alpha m(x) u^+ - beta m(x) u^- +f(x,u), quad x in Omega, cr frac{partial u}{partial eta} + sigma (x) u =alpha rho (x) u^+- beta rho (x) u^- +g(x,u), quad x in partial Omega, }$$ where ((alpha, beta) in mathbb{R}^2), (c, m in L^infty (Omega)), (sigma, rho in L^infty (partialOmega)), and the nonlinearities f and g are bounded continuous functions. We study the asymmetric (Fucik) spectrum with weights, and prove existence theorems for nonlinear perturbations of this spectrum for both the resonance and non-resonance cases. For the resonance case, we provide a sufficient condition, the so-called generalized Landesman-Lazer condition, for the solvability. The proofs are based on variational methods and rely strongly on the variational characterization of the spectrum.\u0000See also https://ejde.math.txstate.edu/special/02/m2/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48767063","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
Optimal conditions for the maximum principle for second-order periodic problems 二阶周期问题极大值原理的最优条件
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-03-27 DOI: 10.58997/ejde.sp.02.h2
G. Holubová
{"title":"Optimal conditions for the maximum principle for second-order periodic problems","authors":"G. Holubová","doi":"10.58997/ejde.sp.02.h2","DOIUrl":"https://doi.org/10.58997/ejde.sp.02.h2","url":null,"abstract":"We provide alternate necessary and/or sufficient conditions on the  sign-changing coefficient p(t) for the maximum principle for the  second-order periodic problem (u''=p(t) u + q(t) ) to hold, i.e., for nonnegative (q) to yield a nonpositive periodic solution (u).\u0000See also https://ejde.math.txstate.edu/special/02/h2/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48234376","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
Yamabe boundary problem with scalar-flat manifolds target 标量平面流形目标的Yamabe边界问题
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-03-27 DOI: 10.58997/ejde.sp.02.g1
Marco Ghimenti, A. Micheletti
{"title":"Yamabe boundary problem with scalar-flat manifolds target","authors":"Marco Ghimenti, A. Micheletti","doi":"10.58997/ejde.sp.02.g1","DOIUrl":"https://doi.org/10.58997/ejde.sp.02.g1","url":null,"abstract":"We present a survey on the compactness of the set of solutions for the Yamabe problem on manifolds with boundary. The stability of the problem is also discussed.\u0000See also https://ejde.math.txstate.edu/special/02/g1/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43969984","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
Nonlinear diffusion with the p-Laplacian in a Black-Scholes-type model Black-Scholes型模型中p-拉普拉斯算子的非线性扩散
IF 0.7 4区 数学
Electronic Journal of Differential Equations Pub Date : 2023-03-27 DOI: 10.58997/ejde.sp.02.t1
P. Takáč
{"title":"Nonlinear diffusion with the p-Laplacian in a Black-Scholes-type model","authors":"P. Takáč","doi":"10.58997/ejde.sp.02.t1","DOIUrl":"https://doi.org/10.58997/ejde.sp.02.t1","url":null,"abstract":"We present a new nonlinear version of the well-known Black-Scholes model for option pricing in financial mathematics. The nonlinear Black-Scholes partial differential equation is based on the quasilinear diffusion term with the p-Laplace operator (Delta_p) for (1 < p < infty). The existence and uniqueness of a weak solution in a weighted Sobolev space is proved, first, by methods for nonlinear parabolic problems using the Gel'fand triplet and,  alternatively, by a method based on nonlinear semigroups. Finally, possible choices of other weighted Sobolev spaces are discussed to produce a function space setting more realistic in financial mathematics.\u0000See also https://ejde.math.txstate.edu/special/02/t1/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49404393","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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