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Nonlinear Differential Equations and Applications (NoDEA)最新文献

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On the one-dimensional Pompeiu problem 关于一维庞培问题
Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-04-15 DOI: 10.1007/s00030-024-00940-9
Vivina Barutello, Camillo Costantini
{"title":"On the one-dimensional Pompeiu problem","authors":"Vivina Barutello, Camillo Costantini","doi":"10.1007/s00030-024-00940-9","DOIUrl":"https://doi.org/10.1007/s00030-024-00940-9","url":null,"abstract":"<p>We investigate the Pompeiu property for subsets of the real line, under no assumption of connectedness. In particular we focus our study on finite unions of bounded (disjoint) intervals, and we emphasize the different results corresponding to the cases where the function in question is supposed to have constant integral on all isometric images, or just on all the translation-images of the domain. While no set of the previous kind enjoys the Pompeiu property in the latter sense, we provide a necessary and sufficient condition in order a union of two intervals to have the Pompeiu property in the former sense, and we produce some examples to give an insight of the complexity of the problem for three-interval sets.\u0000</p>","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140571746","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
A global method for relaxation for multi-levelled structured deformations 多级结构变形的全局松弛法
Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-04-13 DOI: 10.1007/s00030-024-00939-2
Ana Cristina Barroso, José Matias, Elvira Zappale
{"title":"A global method for relaxation for multi-levelled structured deformations","authors":"Ana Cristina Barroso, José Matias, Elvira Zappale","doi":"10.1007/s00030-024-00939-2","DOIUrl":"https://doi.org/10.1007/s00030-024-00939-2","url":null,"abstract":"<p>We prove an integral representation result for a class of variational functionals appearing in the framework of hierarchical systems of structured deformations via a global method for relaxation. Some applications to specific relaxation problems are also provided.\u0000</p>","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"37 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140571752","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
Fast rotation and inviscid limits for the SQG equation with general ill-prepared initial data 具有一般非准备初始数据的 SQG 方程的快速旋转和不粘性极限
Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-04-12 DOI: 10.1007/s00030-024-00942-7
Gabriele Sbaiz, Leonardo Kosloff
{"title":"Fast rotation and inviscid limits for the SQG equation with general ill-prepared initial data","authors":"Gabriele Sbaiz, Leonardo Kosloff","doi":"10.1007/s00030-024-00942-7","DOIUrl":"https://doi.org/10.1007/s00030-024-00942-7","url":null,"abstract":"<p>In the present paper, we study the fast rotation and inviscid limits for the 2-D dissipative surface quasi-geostrophic equation with a dispersive forcing term, in the domain <span>(Omega =mathbb {T}^1times mathbb {R})</span>. In the case when we perform the fast rotation limit (keeping the viscosity fixed), in the context of general ill-prepared initial data, we prove that the limit dynamics is described by a linear equation with parabolic structure. Conversely, performing the combined fast rotation and inviscid limits, we show that the means of the target initial datum <span>(overline{vartheta }_0)</span> are conserved along the motion. The proof of the convergence is based on a compensated compactness argument which allows, on the one hand, to get compactness properties for suitable quantities hidden in the wave system and, on the other hand, to exclude the oscillatory part of waves at the limit.</p>","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"44 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140571571","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
Global solutions to the Kirchhoff equation with spectral gap data in the energy space 基尔霍夫方程的全局解与能量空间的谱隙数据
Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-04-11 DOI: 10.1007/s00030-024-00933-8
Marina Ghisi, Massimo Gobbino
{"title":"Global solutions to the Kirchhoff equation with spectral gap data in the energy space","authors":"Marina Ghisi, Massimo Gobbino","doi":"10.1007/s00030-024-00933-8","DOIUrl":"https://doi.org/10.1007/s00030-024-00933-8","url":null,"abstract":"<p>We prove that the classical hyperbolic Kirchhoff equation admits global-in-time solutions for some classes of initial data in the energy space. We also show that there are enough such solutions so that every initial datum in the energy space is the sum of two initial data for which a global-in-time solution exists. The proof relies on the notion of spectral gap data, namely initial data whose components vanish for large intervals of frequencies. We do not pass through the linearized equation, because it is not well-posed at this low level of regularity.</p>","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"208 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140571744","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
Global dynamics of a two-species clustering model with Lotka–Volterra competition 具有洛特卡-伏特拉竞争的双物种聚类模型的全局动力学
Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-04-09 DOI: 10.1007/s00030-024-00934-7
Weirun Tao, Zhi-An Wang, Wen Yang
{"title":"Global dynamics of a two-species clustering model with Lotka–Volterra competition","authors":"Weirun Tao, Zhi-An Wang, Wen Yang","doi":"10.1007/s00030-024-00934-7","DOIUrl":"https://doi.org/10.1007/s00030-024-00934-7","url":null,"abstract":"<p>This paper is concerned with the global dynamics of a two-species Grindrod clustering model with Lotka–Volterra competition. The model takes the advective flux to depend directly upon local population densities without requiring intermediate signals like attractants or repellents to form the aggregation so as to increase the chances of survival of individuals like human populations forming small nucleated settlements. By imposing appropriate boundary conditions, we establish the global boundedness of solutions in two-dimensional bounded domains. Moreover, we prove the global stability of spatially homogeneous steady states under appropriate conditions on system parameters, and show that the rate of convergence to the coexistence steady state is exponential while the rate of convergence to the competitive exclusion steady state is algebraic.</p>","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"108 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140571561","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 of bound states for quasilinear elliptic problems involving critical growth and frequency 涉及临界增长和频率的准线性椭圆问题约束状态的存在性
Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-04-02 DOI: 10.1007/s00030-024-00932-9
{"title":"Existence of bound states for quasilinear elliptic problems involving critical growth and frequency","authors":"","doi":"10.1007/s00030-024-00932-9","DOIUrl":"https://doi.org/10.1007/s00030-024-00932-9","url":null,"abstract":"<h3>Abstract</h3> <p>In this paper we study the existence of bound states for the following class of quasilinear problems, <span> <span>$$begin{aligned} left{ begin{aligned}&amp;-varepsilon ^pDelta _pu+V(x)u^{p-1}=f(u)+u^{p^*-1}, u&gt;0, text {in} {mathbb {R}}^{N},&amp;lim _{|x|rightarrow infty }u(x) = 0, end{aligned} right. end{aligned}$$</span> </span>where <span> <span>(varepsilon &gt;0)</span> </span> is small, <span> <span>(1&lt;p&lt;N,)</span> </span> <em>f</em> is a nonlinearity with general subcritical growth in the Sobolev sense, <span> <span>(p^{*} = pN/(N-p))</span> </span> and <em>V</em> is a continuous nonnegative potential. By introducing a new set of hypotheses, our analysis includes the critical frequency case which allows the potential <em>V</em> to not be necessarily bounded below away from zero. We also study the regularity and behavior of positive solutions as <span> <span>(|x|rightarrow infty )</span> </span> or <span> <span>(varepsilon rightarrow 0,)</span> </span> proving that they are uniformly bounded and concentrate around suitable points of <span> <span>({mathbb {R}}^N,)</span> </span> that may include local minima of <em>V</em>.</p>","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"50 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140571719","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
Two-phase almost minimizers for a fractional free boundary problem 分数自由边界问题的两相几乎最小化
Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-04-01 DOI: 10.1007/s00030-024-00937-4
Mark Allen, Mariana Smit Vega Garcia
{"title":"Two-phase almost minimizers for a fractional free boundary problem","authors":"Mark Allen, Mariana Smit Vega Garcia","doi":"10.1007/s00030-024-00937-4","DOIUrl":"https://doi.org/10.1007/s00030-024-00937-4","url":null,"abstract":"<p>In this paper, we study almost minimizers to a fractional Alt–Caffarelli–Friedman type functional. Our main results concern the optimal <span>(C^{0,s})</span> regularity of almost minimizers as well as the structure of the free boundary. We first prove that the two free boundaries <span>(F^+(u)=partial {u(cdot ,0)&gt;0})</span> and <span>(F^-(u)=partial {u(cdot ,0)&lt;0})</span> cannot touch, that is, <span>(F^+(u)cap F^-(u)=emptyset )</span>. Lastly, we prove a flatness implies <span>(C^{1,gamma })</span> result for the free boundary.</p>","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"84 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140571745","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
Semilinear elliptic problems in $$mathbb {R}^N$$ : the interplay between the potential and the nonlinear term $$mathbb {R}^N$$ 中的半线性椭圆问题：势与非线性项之间的相互作用
Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-03-28 DOI: 10.1007/s00030-024-00938-3
Elves Alves de Barros e Silva, Sergio H. Monari Soares
{"title":"Semilinear elliptic problems in $$mathbb {R}^N$$ : the interplay between the potential and the nonlinear term","authors":"Elves Alves de Barros e Silva, Sergio H. Monari Soares","doi":"10.1007/s00030-024-00938-3","DOIUrl":"https://doi.org/10.1007/s00030-024-00938-3","url":null,"abstract":"<p>It is considered a semilinear elliptic partial differential equation in <span>(mathbb {R}^N)</span> with a potential that may vanish at infinity and a nonlinear term with subcritical growth. A positive solution is proved to exist depending on the interplay between the decay of the potential at infinity and the behavior of the nonlinear term at the origin. The proof is based on a penalization argument, variational methods, and <span>(L^infty )</span> estimates. Those estimates allow dealing with settings where the nonlinear source may have supercritical, critical, or subcritical behavior near the origin. Results that provide the existence of multiple and infinitely many solutions when the nonlinear term is odd are also established.</p>","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"56 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140322394","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
Simple Lyapunov spectrum for linear homogeneous differential equations with $$L^p$$ parameters 参数为 $$L^p$$ 的线性均质微分方程的简单 Lyapunov 谱
Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-03-24 DOI: 10.1007/s00030-024-00931-w
Dinis Amaro, Mário Bessa, Helder Vilarinho
{"title":"Simple Lyapunov spectrum for linear homogeneous differential equations with $$L^p$$ parameters","authors":"Dinis Amaro, Mário Bessa, Helder Vilarinho","doi":"10.1007/s00030-024-00931-w","DOIUrl":"https://doi.org/10.1007/s00030-024-00931-w","url":null,"abstract":"<p>In the present paper we prove that densely, with respect to an <span>(L^p)</span>-like topology, the Lyapunov exponents associated to linear continuous-time cocycles <span>(Phi :mathbb {R}times Mrightarrow {{,textrm{GL},}}(2,mathbb {R}))</span> induced by second order linear homogeneous differential equations <span>(ddot{x}+alpha (varphi ^t(omega ))dot{x}+beta (varphi ^t(omega ))x=0)</span> are almost everywhere distinct. The coefficients <span>(alpha ,beta )</span> evolve along the <span>(varphi ^t)</span>-orbit for <span>(omega in M)</span> and <span>(varphi ^t: Mrightarrow M)</span> is an ergodic flow defined on a probability space. We also obtain the corresponding version for the frictionless equation <span>(ddot{x}+beta (varphi ^t(omega ))x=0)</span> and for a Schrödinger equation <span>(ddot{x}+(E-Q(varphi ^t(omega )))x=0)</span>, inducing a cocycle <span>(Phi :mathbb {R}times Mrightarrow {{,textrm{SL},}}(2,mathbb {R}))</span>.\u0000</p>","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"32 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140301531","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
A symmetry result for fully nonlinear problems in exterior domains 外域中全非线性问题的对称性结果
Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-03-23 DOI: 10.1007/s00030-024-00930-x
David Stolnicki
{"title":"A symmetry result for fully nonlinear problems in exterior domains","authors":"David Stolnicki","doi":"10.1007/s00030-024-00930-x","DOIUrl":"https://doi.org/10.1007/s00030-024-00930-x","url":null,"abstract":"<p>We study an overdetermined fully nonlinear problem driven by one of the Pucci’s Extremal Operators in an external domain. Under certain decay assumptions on the solution, we extend Serrin’s symmetry result, i.e, every domain where the solution exists must be radial.</p>","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"40 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140201730","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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