In this article, we consider an inverse nodal problem of Dirac operators and obtain approximate solution and its convergence based on the second kind Chebyshev wavelet and Bernstein methods. We establish a uniqueness theorem of this problem from parts of nodal points instead of a dense nodal set. Numerical examples are carried out to illustrate our method. For more information see https://ejde.math.txstate.edu/Volumes/2023/81/abstr.html
{"title":"Inverse nodal problems for Dirac operators and their numerical approximations","authors":"Fei Song, Yu-Ping Wang, S. Akbarpoor","doi":"10.58997/ejde.2023.81","DOIUrl":"https://doi.org/10.58997/ejde.2023.81","url":null,"abstract":"In this article, we consider an inverse nodal problem of Dirac operators and obtain approximate solution and its convergence based on the second kind Chebyshev wavelet and Bernstein methods. We establish a uniqueness theorem of this problem from parts of nodal points instead of a dense nodal set. Numerical examples are carried out to illustrate our method. \u0000For more information see https://ejde.math.txstate.edu/Volumes/2023/81/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":"7 9","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138594244","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}
M. Barkatou, Félix Álvaro Carnicero, Fernando Sanz
We establish a version of Turrittin's result on normal forms of linear systems of meromorphic ODEs when the base field K is real and closed. Both the proposed normal forms and the transformations used have coefficients in K. Our motivation comes from applications to the study of trajectories of real analytic vector fields (already treated in the literature in dimension three). For the sake of clarity and completeness, we first review Turrittin's theorem in the case of an algebraically closed base field. For more information see https://ejde.math.txstate.edu/Volumes/2023/79/abstr.html
当基场 K 为实且闭时，我们建立了 Turrittin 关于分形 ODE 线性系统正常形式结果的一个版本。我们的动机来自于对实解析向量场轨迹研究的应用（在三维文献中已有论述）。为了清晰和完整起见，我们首先回顾一下代数封闭基场情况下的 Turrittin 定理。更多信息，请参见 https://ejde.math.txstate.edu/Volumes/2023/79/abstr.html
{"title":"Turrittin's normal forms for linear systems of meromorphic ODEs over the real field","authors":"M. Barkatou, Félix Álvaro Carnicero, Fernando Sanz","doi":"10.58997/ejde.2023.79","DOIUrl":"https://doi.org/10.58997/ejde.2023.79","url":null,"abstract":"We establish a version of Turrittin's result on normal forms of linear systems of meromorphic ODEs when the base field K is real and closed. Both the proposed normal forms and the transformations used have coefficients in K. Our motivation comes from applications to the study of trajectories of real analytic vector fields (already treated in the literature in dimension three). For the sake of clarity and completeness, we first review Turrittin's theorem in the case of an algebraically closed base field. For more information see https://ejde.math.txstate.edu/Volumes/2023/79/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":"12 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139231298","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}
Wilberclay G. Melo, Nata F. Rocha, Natielle dos Santos Costa
In this article, we prove the existence of a unique global solution for the critical case of the generalized Navier-Stokes equations in Lei-Lin and Lei-Lin-Gevrey spaces, by assuming that the initial data is small enough. Moreover, we obtain a unique local solution for the subcritical case of this system, for any initial data, in these same spaces. It is important to point out that our main result is obtained by discussing some properties of the solutions for the heat equation with fractional dissipation.
For more information see https://ejde.math.txstate.edu/Volumes/2023/78/abstr.html
{"title":"Solutions for the Navier-Stokes equations with critical and subcritical fractional dissipation in Lei-Lin and Lei-Lin-Gevrey spaces","authors":"Wilberclay G. Melo, Nata F. Rocha, Natielle dos Santos Costa","doi":"10.58997/ejde.2023.78","DOIUrl":"https://doi.org/10.58997/ejde.2023.78","url":null,"abstract":"In this article, we prove the existence of a unique global solution for the critical case of the generalized Navier-Stokes equations in Lei-Lin and Lei-Lin-Gevrey spaces, by assuming that the initial data is small enough. Moreover, we obtain a unique local solution for the subcritical case of this system, for any initial data, in these same spaces. It is important to point out that our main result is obtained by discussing some properties of the solutions for the heat equation with fractional dissipation.
 For more information see https://ejde.math.txstate.edu/Volumes/2023/78/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":" 1074","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135186457","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}
In this article, we study existence and stability of ground states for a system of two coupled nonlinear Schrodinger equations with logarithmic nonlinearity. Moreover, global well-posedness is verified for the Cauchy problem in (H^{1}(mathbb{R})times H^{1}(mathbb{R})) and in an appropriate Orlicz space.
For more information see https://ejde.math.txstate.edu/Volumes/2023/76/abstr.html
{"title":"Stability of ground states of nonlinear Schrodinger systems","authors":"Liliana Cely","doi":"10.58997/ejde.2023.76","DOIUrl":"https://doi.org/10.58997/ejde.2023.76","url":null,"abstract":"In this article, we study existence and stability of ground states for a system of two coupled nonlinear Schrodinger equations with logarithmic nonlinearity. Moreover, global well-posedness is verified for the Cauchy problem in (H^{1}(mathbb{R})times H^{1}(mathbb{R})) and in an appropriate Orlicz space.
 For more information see https://ejde.math.txstate.edu/Volumes/2023/76/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":"241 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135371150","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}
In this article concerns the semiclassical Choquard equation (-varepsilon^2 Delta u +V(x)u = varepsilon^{-2}( frac{1}{|cdot|}* u^2)u) for (x in mathbb{R}^3) and small (varepsilon). We establish the existence of a sequence of localized nodal solutions concentrating near a given local minimum point of the potential function (V), by means of the perturbation method and the method of invariant sets of descending flow. For more information see https://ejde.math.txstate.edu/Volumes/2023/75/abstr.html
本文讨论了(x in mathbb{R}^3)和小(varepsilon)的半经典Choquard方程(-varepsilon^2 Delta u +V(x)u = varepsilon^{-2}( frac{1}{|cdot|}* u^2)u)。利用微扰法和降流不变集法，建立了集中于势函数(V)的一个给定局部极小点附近的一个局部节点解序列的存在性。欲了解更多信息，请参阅https://ejde.math.txstate.edu/Volumes/2023/75/abstr.html
{"title":"Concentration of nodal solutions for semiclassical quadratic Choquard equations","authors":"Lu Yang, Xiangqing Liu, Jianwen Zhou","doi":"10.58997/ejde.2023.75","DOIUrl":"https://doi.org/10.58997/ejde.2023.75","url":null,"abstract":"In this article concerns the semiclassical Choquard equation (-varepsilon^2 Delta u +V(x)u = varepsilon^{-2}( frac{1}{|cdot|}* u^2)u) for (x in mathbb{R}^3) and small (varepsilon). We establish the existence of a sequence of localized nodal solutions concentrating near a given local minimum point of the potential function (V), by means of the perturbation method and the method of invariant sets of descending flow. For more information see https://ejde.math.txstate.edu/Volumes/2023/75/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":"431 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136069114","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}
Bilender P. Allahverdiev, Huseyin Tuna, Hamlet A Isayev
This article concerns a regular $q$-Dirac system under impulsive conditions. We study the existence of solutions, symmetry of the corresponding operator, eigenvalues and eigenfunctions of the system. Also we obtain Green's function and its basic properties. For more informatin see https://ejde.math.txstate.edu/Volumes/2023/74/abstr.html
{"title":"Impulsive regular q-Dirac systems","authors":"Bilender P. Allahverdiev, Huseyin Tuna, Hamlet A Isayev","doi":"10.58997/ejde.2023.74","DOIUrl":"https://doi.org/10.58997/ejde.2023.74","url":null,"abstract":"This article concerns a regular $q$-Dirac system under impulsive conditions. We study the existence of solutions, symmetry of the corresponding operator, eigenvalues and eigenfunctions of the system. Also we obtain Green's function and its basic properties. For more informatin see https://ejde.math.txstate.edu/Volumes/2023/74/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":"4 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136317156","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}
Oulia Bouhoufani, Salim A. Messaoudi, Mostafa Zahri
In this article, we consider a coupled system of two hyperbolic equations with variable exponents in the damping and source terms, where the dampings are modilated with time-dependent coefficients (alpha(t), beta(t)). First, we state and prove an existence result of a global weak solution, using Galerkin's method with compactness arguments. Then, by a Lemma due to Martinez, we establish the decay rates of the solution energy, under suitable assumptions on the variable exponents (m) and (r) and the coefficients ( alpha) and (beta). To illustrate our theoretical results, we give some numerical examples.
For more information see https://ejde.math.txstate.edu/Volumes/2023/73/abstr.html
{"title":"Existence and decay of solutions to coupled systems of nonlinear wave equations with variable exponents","authors":"Oulia Bouhoufani, Salim A. Messaoudi, Mostafa Zahri","doi":"10.58997/ejde.2023.73","DOIUrl":"https://doi.org/10.58997/ejde.2023.73","url":null,"abstract":"In this article, we consider a coupled system of two hyperbolic equations with variable exponents in the damping and source terms, where the dampings are modilated with time-dependent coefficients (alpha(t), beta(t)). First, we state and prove an existence result of a global weak solution, using Galerkin's method with compactness arguments. Then, by a Lemma due to Martinez, we establish the decay rates of the solution energy, under suitable assumptions on the variable exponents (m) and (r) and the coefficients ( alpha) and (beta). To illustrate our theoretical results, we give some numerical examples.
 For more information see https://ejde.math.txstate.edu/Volumes/2023/73/abstr.html
","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135315785","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}
We study the existence and qualitative properties of solutions to the Cauchy problem associated to the quasilinear reaction-diffusion equation $$ partial_tu=Delta u^m+(1+|x|)^{sigma}u^p, $$ posed for ((x,t)inmathbb{R}^Ntimes(0,infty)), where (m>1), (pin(0,1)) and (sigma>0). Initial data are taken to be bounded, non-negative and compactly supported. In the range when (m+pgeq2), we prove existence of local solutions with a finite speed of propagation of their supports for compactly supported initial conditions. We also show in this case that, for a given compactly supported initial condition, there exist infinitely many solutions to the Cauchy problem, by prescribing the evolution of their interface. In the complementary range (m+p<2), we obtain new Aronson-Benilan estimates satisfied by solutions to the Cauchy problem, which are of independent interest as a priori bounds for the solutions. We apply these estimates to establish infinite speed of propagation of the supports of solutions if (m+p<2), that is, (u(x,t)>0) for any (xinmathbb{R}^N), (t>0), even in the case when the initial condition (u_0) is compactly supported. For more information see https://ejde.math.txstate.edu/Volumes/2023/72/abstr.html
{"title":"Qualitative properties of solutions to a reaction-diffusion equation with weighted strong reaction","authors":"Razvan Gabriel Iagar, Ana I. Munoz, Ariel Sanchez","doi":"10.58997/ejde.2023.72","DOIUrl":"https://doi.org/10.58997/ejde.2023.72","url":null,"abstract":"We study the existence and qualitative properties of solutions to the Cauchy problem associated to the quasilinear reaction-diffusion equation $$ partial_tu=Delta u^m+(1+|x|)^{sigma}u^p, $$ posed for ((x,t)inmathbb{R}^Ntimes(0,infty)), where (m>1), (pin(0,1)) and (sigma>0). Initial data are taken to be bounded, non-negative and compactly supported. In the range when (m+pgeq2), we prove existence of local solutions with a finite speed of propagation of their supports for compactly supported initial conditions. We also show in this case that, for a given compactly supported initial condition, there exist infinitely many solutions to the Cauchy problem, by prescribing the evolution of their interface. In the complementary range (m+p<2), we obtain new Aronson-Benilan estimates satisfied by solutions to the Cauchy problem, which are of independent interest as a priori bounds for the solutions. We apply these estimates to establish infinite speed of propagation of the supports of solutions if (m+p<2), that is, (u(x,t)>0) for any (xinmathbb{R}^N), (t>0), even in the case when the initial condition (u_0) is compactly supported. For more information see https://ejde.math.txstate.edu/Volumes/2023/72/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":"47 9","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135414856","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}
The aim of this note is to prove a characterization of the G-limit of a sequence of elliptic operators in non-divergence form. As we consider any dimension, for this class of operators, it is not enough to deal with measurable and bounded coefficients so we need extra regularity assumptions on them.
For more information see https://ejde.math.txstate.edu/Volumes/2023/71/abstr.html
{"title":"G-convergence of elliptic operators in non divergence form in R^n","authors":"Luigi D'Onofrio","doi":"10.58997/ejde.2023.71","DOIUrl":"https://doi.org/10.58997/ejde.2023.71","url":null,"abstract":"The aim of this note is to prove a characterization of the G-limit of a sequence of elliptic operators in non-divergence form. As we consider any dimension, for this class of operators, it is not enough to deal with measurable and bounded coefficients so we need extra regularity assumptions on them.
 For more information see https://ejde.math.txstate.edu/Volumes/2023/71/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135618836","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}
We study lower bounds at infinity for solutions to $$ |Pu|leq M|x|^{-delta_1}|nabla u|+M|x|^{-delta_{0}}|u| $$ where $P$ is a second order elliptic operator. Our results are of quantitative nature and generalize those obtained in [3,6].
For more information see https://ejde.math.txstate.edu/Volumes/2023/69/abstr.html
{"title":"Lower bounds at infinity for solutions to second order elliptic equations","authors":"Tu Nguyen","doi":"10.58997/ejde.2023.69","DOIUrl":"https://doi.org/10.58997/ejde.2023.69","url":null,"abstract":"We study lower bounds at infinity for solutions to $$ |Pu|leq M|x|^{-delta_1}|nabla u|+M|x|^{-delta_{0}}|u| $$ where $P$ is a second order elliptic operator. Our results are of quantitative nature and generalize those obtained in [3,6].
 For more information see https://ejde.math.txstate.edu/Volumes/2023/69/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":"223 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136142329","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}
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