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Nonlinear Differential Equations and Applications (NoDEA)最新文献

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Annular type surfaces with fixed boundary and with prescribed, almost constant mean curvature 具有固定边界和规定的几乎恒定的平均曲率的环形曲面
Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-01-25 DOI: 10.1007/s00030-023-00915-2
Paolo Caldiroli, Gabriele Cora, Alessandro Iacopetti
{"title":"Annular type surfaces with fixed boundary and with prescribed, almost constant mean curvature","authors":"Paolo Caldiroli, Gabriele Cora, Alessandro Iacopetti","doi":"10.1007/s00030-023-00915-2","DOIUrl":"https://doi.org/10.1007/s00030-023-00915-2","url":null,"abstract":"<p>We prove existence and nonexistence results for annular type parametric surfaces with prescribed, almost constant mean curvature, characterized as normal graphs of compact portions of unduloids or nodoids in <span>({mathbb {R}}^{3})</span>, and whose boundary consists of two coaxial circles of the same radius.</p>","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"171 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139553969","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
On radial positive normalized solutions of the Nonlinear Schrödinger equation in an annulus 论环面非线性薛定谔方程的径向正归一化解
Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-01-22 DOI: 10.1007/s00030-023-00917-0
Jian Liang, Linjie Song
{"title":"On radial positive normalized solutions of the Nonlinear Schrödinger equation in an annulus","authors":"Jian Liang, Linjie Song","doi":"10.1007/s00030-023-00917-0","DOIUrl":"https://doi.org/10.1007/s00030-023-00917-0","url":null,"abstract":"<p>We are interested in the following semilinear elliptic problem: </p><span>$$begin{aligned} {left{ begin{array}{ll} -Delta u + lambda u = u^{p-1}, x in T, u &gt; 0, u = 0 text {on} partial T, int _{T}u^{2} , dx= c end{array}right. } end{aligned}$$</span><p>where <span>(T = {x in mathbb {R}^{N}: 1&lt; |x| &lt; 2})</span> is an annulus in <span>(mathbb {R}^{N})</span>, <span>(N ge 2)</span>, <span>(p &gt; 1)</span> is Sobolev-subcritical, searching for conditions (about <i>c</i>, <i>N</i> and <i>p</i>) for the existence of positive radial solutions. We analyze the asymptotic behavior of <i>c</i> as <span>(lambda rightarrow +infty )</span> and <span>(lambda rightarrow -lambda _1)</span> to get the existence, non-existence and multiplicity of normalized solutions. Additionally, based on the properties of these solutions, we extend the results obtained in Pierotti et al. in Calc Var Partial Differ Equ 56:1–27, 2017. In contrast of the earlier results, a positive radial solution with arbitrarily large mass can be obtained when <span>(N ge 3)</span> or if <span>(N = 2)</span> and <span>(p &lt; 6)</span>. Our paper also includes the demonstration of orbital stability/instability results.\u0000</p>","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139553971","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
Optimization of the Dirichlet problem for gradient differential inclusions 梯度微分夹杂的德里赫特问题优化
Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-01-20 DOI: 10.1007/s00030-023-00904-5
Elimhan N. Mahmudov, Dilara Mastaliyeva
{"title":"Optimization of the Dirichlet problem for gradient differential inclusions","authors":"Elimhan N. Mahmudov, Dilara Mastaliyeva","doi":"10.1007/s00030-023-00904-5","DOIUrl":"https://doi.org/10.1007/s00030-023-00904-5","url":null,"abstract":"<p>The paper is devoted to optimization of the gradient differential inclusions (DFIs) on a rectangular area. The discretization method is the main method for solving the proposed boundary value problem. For the transition from discrete to continuous, a specially proven equivalence theorem is provided. To optimize the posed continuous gradient DFIs, a passage to the limit is required in the discrete-approximate problem. Necessary and sufficient conditions of optimality for such problems are derived in the Euler–Lagrange form. The results obtained in terms of the divergence operation of the Euler–Lagrange adjoint inclusion are extended to the multidimensional case. Such results are based on locally adjoint mappings, being related coderivative concept of Mordukhovich.\u0000</p>","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139506991","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
Fujita-type results for the degenerate parabolic equations on the Heisenberg groups 海森堡群上退化抛物方程的富士达型结果
Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-01-20 DOI: 10.1007/s00030-023-00907-2
Ahmad Z. Fino, Michael Ruzhansky, Berikbol T. Torebek
{"title":"Fujita-type results for the degenerate parabolic equations on the Heisenberg groups","authors":"Ahmad Z. Fino, Michael Ruzhansky, Berikbol T. Torebek","doi":"10.1007/s00030-023-00907-2","DOIUrl":"https://doi.org/10.1007/s00030-023-00907-2","url":null,"abstract":"<p>In this paper, we consider the Cauchy problem for the degenerate parabolic equations on the Heisenberg groups with power law non-linearities. We obtain Fujita-type critical exponents, which depend on the homogeneous dimension of the Heisenberg groups. The analysis includes the case of porous medium equations. Our proof approach is based on methods of nonlinear capacity estimates specifically adapted to the nature of the Heisenberg groups. We also use the Kaplan eigenfunctions method in combination with the Hopf-type lemma on the Heisenberg groups.</p>","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139506993","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
Boundedness of solutions to a chemotaxis–haptotaxis model with nonlocal terms 具有非局部项的趋化-aptotaxis模型解的有界性
Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-01-06 DOI: 10.1007/s00030-023-00908-1
Guoqiang Ren
{"title":"Boundedness of solutions to a chemotaxis–haptotaxis model with nonlocal terms","authors":"Guoqiang Ren","doi":"10.1007/s00030-023-00908-1","DOIUrl":"https://doi.org/10.1007/s00030-023-00908-1","url":null,"abstract":"<p>In this paper, we consider the chemotaxis–haptotaxis model of two different types (parabolic–elliptic, fully parabolic) with nonlocal terms under Neumann boundary conditions in a bounded domain with smooth boundary. We show that the system possesses a unique global classical solution in different cases. Our results generalize and improve partial previously known ones.</p>","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"68 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139373241","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
On a characterization of the Rellich–Kondrachov theorem on groups and the Bloch spectral cell equation 关于群上的雷利奇-康德拉乔夫定理的特征和布洛赫谱单元方程
Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-01-03 DOI: 10.1007/s00030-023-00905-4
Vernny Ccajma, Wladimir Neves, Jean Silva
{"title":"On a characterization of the Rellich–Kondrachov theorem on groups and the Bloch spectral cell equation","authors":"Vernny Ccajma, Wladimir Neves, Jean Silva","doi":"10.1007/s00030-023-00905-4","DOIUrl":"https://doi.org/10.1007/s00030-023-00905-4","url":null,"abstract":"<p>This paper is concerned with the Rellich–Kondrachov Theorem on Groups. We establish some conditions which characterize in a precise manner important properties related to this theorem and the Sobolev spaces on groups involved on it. The main motivation to study the Rellich–Kondrachov Theorem on Groups comes from the Bloch spectral cell equation, which is an eigenvalue-eigenfunction problem associated with the assymptotic limit of the anisotropic Schrödinger equation.</p>","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"74 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139105325","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
Liouville-type theorems for fractional Hardy–Hénon systems 分数 Hardy-Hénon 系统的 Liouville 型定理
Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2023-12-28 DOI: 10.1007/s00030-023-00903-6
Kui Li, Meng Yu, Zhitao Zhang
{"title":"Liouville-type theorems for fractional Hardy–Hénon systems","authors":"Kui Li, Meng Yu, Zhitao Zhang","doi":"10.1007/s00030-023-00903-6","DOIUrl":"https://doi.org/10.1007/s00030-023-00903-6","url":null,"abstract":"<p>In this paper, we study Liouville-type theorems for fractional Hardy–Hénon elliptic systems with weights. Because the weights are singular at zero, we firstly prove that classical solutions for systems in <span>({mathbb {R}}^N backslash {0})</span> are also distributional solutions in <span>({mathbb {R}}^N)</span>. Then we study the equivalence between the fractional Hardy–Hénon system and a proper integral system, and we obtain new Liouville-type theorems for supersolutions and solutions by the method of integral estimates and scaling spheres respectively.\u0000</p>","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139071746","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
The continuous dependence of the viscous Boussinesq equations uniformly with respect to the viscosity 粘滞布森斯克方程与粘度的均匀连续相关性
Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2023-12-27 DOI: 10.1007/s00030-023-00902-7
Rong Chen, Zhichun Yang, Shouming Zhou
{"title":"The continuous dependence of the viscous Boussinesq equations uniformly with respect to the viscosity","authors":"Rong Chen, Zhichun Yang, Shouming Zhou","doi":"10.1007/s00030-023-00902-7","DOIUrl":"https://doi.org/10.1007/s00030-023-00902-7","url":null,"abstract":"<p>This paper focuses on the inviscid limit of the incompressible Boussinesq equations in the same topology as the initial data, and proved that the continuous dependence of the viscous Boussinesq equations uniformly in some Besov spaces with respect to the viscosity. Our results extends the work of Guo et al. (J Funct Anal 276(9):2821–2830, 2019) on Navier–Stokes equations to Boussinesq equations with both stratified limit and earth’s rotation.</p>","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139051844","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
Evolutionary stable strategies and cubic vector fields 进化稳定策略和立方向量场
Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2023-12-26 DOI: 10.1007/s00030-023-00894-4
Jefferson Bastos, Claudio Buzzi, Paulo Santana
{"title":"Evolutionary stable strategies and cubic vector fields","authors":"Jefferson Bastos, Claudio Buzzi, Paulo Santana","doi":"10.1007/s00030-023-00894-4","DOIUrl":"https://doi.org/10.1007/s00030-023-00894-4","url":null,"abstract":"<p>The introduction of concepts of Game Theory and Ordinary Differential Equations into Biology gave birth to the field of Evolutionary Stable Strategies, with applications in Biology, Genetics, Politics, Economics and others. In special, the model composed by two players having two pure strategies each results in a planar cubic vector field with an invariant octothorpe. Therefore, in this paper we study such class of vector fields, suggesting the notion of genericity and providing the global phase portraits of the generic systems with a singularity at the central region of the octothorpe.</p>","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139051837","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 non-existence results for cooperative elliptic systems without variational structure 无变结构合作椭圆系统的存在与不存在结果
Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2023-12-15 DOI: 10.1007/s00030-023-00896-2
John Villavert
{"title":"Existence and non-existence results for cooperative elliptic systems without variational structure","authors":"John Villavert","doi":"10.1007/s00030-023-00896-2","DOIUrl":"https://doi.org/10.1007/s00030-023-00896-2","url":null,"abstract":"<p>We consider general cooperative elliptic systems possibly without variational structure and with differential operator resembling that from an Euler–Lagrange equation for a sharp Hardy–Sobolev inequality. Under suitable growth conditions on the source nonlinearities and geometric assumptions on the domain, we derive various existence and non-existence results and Liouville theorems. The results are obtained by incorporating and adapting various techniques, including variants of the method of moving planes enhanced by Kelvin and Emden–Fowler type transformations, as well as degree theoretic shooting methods.</p>","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"76 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138682637","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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