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Nonlinear Differential Equations and Applications (NoDEA)最新文献

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Boundary value problems associated with Hamiltonian systems coupled with positively-(p, q)-homogeneous systems 与正-(p, q)-均质系统耦合的哈密顿系统相关的边值问题
Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-03-20 DOI: 10.1007/s00030-024-00925-8
{"title":"Boundary value problems associated with Hamiltonian systems coupled with positively-(p, q)-homogeneous systems","authors":"","doi":"10.1007/s00030-024-00925-8","DOIUrl":"https://doi.org/10.1007/s00030-024-00925-8","url":null,"abstract":"<h3>Abstract</h3> <p>We study the multiplicity of solutions for a two-point boundary value problem of Neumann type associated with a Hamiltonian system which couples a system with periodic Hamiltonian in the space variable with a second one with positively-(<em>p</em>, <em>q</em>)-homogeneous Hamiltonian. The periodic problem is also treated.</p>","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"39 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140201732","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
Gradient higher integrability for singular parabolic double-phase systems 奇异抛物线双相系统的梯度高积分性
Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-03-15 DOI: 10.1007/s00030-024-00928-5
{"title":"Gradient higher integrability for singular parabolic double-phase systems","authors":"","doi":"10.1007/s00030-024-00928-5","DOIUrl":"https://doi.org/10.1007/s00030-024-00928-5","url":null,"abstract":"<h3>Abstract</h3> <p>We prove a local higher integrability result for the gradient of a weak solution to parabolic double-phase systems of <em>p</em>-Laplace type when <span> <span>(tfrac{2n}{n+2}&lt; ple 2)</span> </span>. The result is based on a reverse Hölder inequality in intrinsic cylinders combining <em>p</em>-intrinsic and (<em>p</em>, <em>q</em>)-intrinsic geometries. A singular scaling deficits affects the range of <em>q</em>.</p>","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140152137","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
Singular solutions of semilinear elliptic equations with supercritical growth on Riemannian manifolds 黎曼流形上超临界增长的半线性椭圆方程的奇异解
Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-03-14 DOI: 10.1007/s00030-024-00926-7
Shoichi Hasegawa
{"title":"Singular solutions of semilinear elliptic equations with supercritical growth on Riemannian manifolds","authors":"Shoichi Hasegawa","doi":"10.1007/s00030-024-00926-7","DOIUrl":"https://doi.org/10.1007/s00030-024-00926-7","url":null,"abstract":"<p>In this paper, we shall discuss singular solutions of semilinear elliptic equations with general supercritical growth on spherically symmetric Riemannian manifolds. More precisely, we shall prove the existence, uniqueness and asymptotic behavior of the singular radial solution, and also show that regular radial solutions converges to the singular solution. In particular, we shall provide these properties on spherically symmetric Riemannian manifolds including the hyperbolic space as well as the sphere.</p>","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"60 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140152135","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
Unified results for existence and compactness in the prescribed fractional Q-curvature problem 规定分数 Q曲率问题中存在性和紧凑性的统一结果
Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-03-13 DOI: 10.1007/s00030-024-00927-6
Yan Li, Zhongwei Tang, Heming Wang, Ning Zhou
{"title":"Unified results for existence and compactness in the prescribed fractional Q-curvature problem","authors":"Yan Li, Zhongwei Tang, Heming Wang, Ning Zhou","doi":"10.1007/s00030-024-00927-6","DOIUrl":"https://doi.org/10.1007/s00030-024-00927-6","url":null,"abstract":"<p>In this paper we study the problem of prescribing fractional <i>Q</i>-curvature of order <span>(2sigma )</span> for a conformal metric on the standard sphere <span>(mathbb {S}^n)</span> with <span>(sigma in (0,n/2))</span> and <span>(nge 3)</span>. Compactness and existence results are obtained in terms of the flatness order <span>(beta )</span> of the prescribed curvature function <i>K</i>. Making use of integral representations and perturbation result, we develop a unified approach to obtain these results when <span>(beta in [n-2sigma ,n))</span> for all <span>(sigma in (0,n/2))</span>. This work generalizes the corresponding results of Jin-Li-Xiong (Math Ann 369:109–151, 2017) for <span>(beta in (n-2sigma ,n))</span>.</p>","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140128307","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 backward Euler approximations for systems of conservation laws 论守恒定律系统的欧拉后向逼近
Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-03-12 DOI: 10.1007/s00030-023-00920-5
Maria Teresa Chiri, Minyan Zhang
{"title":"On backward Euler approximations for systems of conservation laws","authors":"Maria Teresa Chiri, Minyan Zhang","doi":"10.1007/s00030-023-00920-5","DOIUrl":"https://doi.org/10.1007/s00030-023-00920-5","url":null,"abstract":"<p>We study approximate solutions to a hyperbolic system of conservation laws, constructed by a backward Euler scheme, where time is discretized while space is still described by a continuous variable <span>(xin {mathbb R})</span>. We prove the global existence and uniqueness of these approximate solutions, and the invariance of suitable subdomains. Furthermore, given a left and a right state <span>(u_l, u_r)</span> connected by an entropy-admissible shock, we construct a traveling wave profile for the backward Euler scheme connecting these two asymptotic states in two main cases. Namely: (1) a scalar conservation law, where the jump <span>(u_l-u_r)</span> can be arbitrarily large, and (2) a strictly hyperbolic system, assuming that the jump <span>(u_l-u_r)</span> occurs in a genuinely nonlinear family and is sufficiently small.</p>","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140128234","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 convergence rate of periodic homogenization for forced mean curvature flow of graphs in the laminar setting 层流背景下图形受迫平均曲率流的周期均质化收敛率
Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-03-09 DOI: 10.1007/s00030-024-00929-4
{"title":"A convergence rate of periodic homogenization for forced mean curvature flow of graphs in the laminar setting","authors":"","doi":"10.1007/s00030-024-00929-4","DOIUrl":"https://doi.org/10.1007/s00030-024-00929-4","url":null,"abstract":"<h3>Abstract</h3> <p>In this paper, we obtain the rate <span> <span>(O(varepsilon ^{1/2}))</span> </span> of convergence in periodic homogenization of forced graphical mean curvature flows in the laminated setting. We also discuss with an example that a faster rate cannot be obtained by utilizing Lipscthiz estimates.</p>","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"45 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140098038","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
Optimal control for the conformal CR sub-Laplacian obstacle problem 保角 CR 子拉普拉斯障碍问题的优化控制
Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-03-04 DOI: 10.1007/s00030-024-00923-w
Pak Tung Ho, Cheikh Birahim Ndiaye
{"title":"Optimal control for the conformal CR sub-Laplacian obstacle problem","authors":"Pak Tung Ho, Cheikh Birahim Ndiaye","doi":"10.1007/s00030-024-00923-w","DOIUrl":"https://doi.org/10.1007/s00030-024-00923-w","url":null,"abstract":"<p>In this paper, we study an optimal control problem associated to the conformal CR sub-Laplacian obstacle problem on a compact pseudohermitian manifold. When the CR Yamabe constant is positive, we show that the optimal controls are equal to their associated optimal states and show the existence of a smooth optimal control which induces a conformal contact form with constant Webster scalar curvature.\u0000</p>","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140032433","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
Stable critical point of the Robin function and bubbling phenomenon for a slightly subcritical elliptic problem 略亚临界椭圆问题的罗宾函数稳定临界点和冒泡现象
Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-02-20 DOI: 10.1007/s00030-024-00921-y
Habib Fourti, Rabeh Ghoudi
{"title":"Stable critical point of the Robin function and bubbling phenomenon for a slightly subcritical elliptic problem","authors":"Habib Fourti, Rabeh Ghoudi","doi":"10.1007/s00030-024-00921-y","DOIUrl":"https://doi.org/10.1007/s00030-024-00921-y","url":null,"abstract":"<p>In this paper, we deal with the boundary value problem <span>(-Delta u= |u|^{4/(n-2)}u/[ln (e+|u|)]^varepsilon )</span> in a bounded smooth domain <span>( Omega )</span> in <span>({mathbb {R}}^n)</span>, <span>(nge 3)</span> with homogenous Dirichlet boundary condition. Here <span>(varepsilon &gt;0)</span>. Clapp et al. (J Differ Equ 275:418–446, 2021) built a family of solution blowing up if <span>(nge 4)</span> and <span>(varepsilon )</span> small enough. They conjectured in their paper the existence of sign changing solutions which blow up and blow down at the same point. Here we give a confirmative answer by proving that our slightly subcritical problem has a solution with the shape of sign changing bubbles concentrating on a stable critical point of the Robin function for <span>(varepsilon )</span> sufficiently small.</p>","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"34 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139918546","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
Three results on the energy conservation for the 3D Euler equations 关于三维欧拉方程能量守恒的三个结果
Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-02-20 DOI: 10.1007/s00030-024-00924-9
{"title":"Three results on the energy conservation for the 3D Euler equations","authors":"","doi":"10.1007/s00030-024-00924-9","DOIUrl":"https://doi.org/10.1007/s00030-024-00924-9","url":null,"abstract":"<h3>Abstract</h3> <p>We consider the 3D Euler equations for incompressible homogeneous fluids and we study the problem of energy conservation for weak solutions in the space-periodic case. First, we prove the energy conservation for a full scale of Besov spaces, by extending some classical results to a wider range of exponents. Next, we consider the energy conservation in the case of conditions on the gradient, recovering some results which were known, up to now, only for the Navier–Stokes equations and for weak solutions of the Leray-Hopf type. Finally, we make some remarks on the Onsager singularity problem, identifying conditions which allow to pass to the limit from solutions of the Navier–Stokes equations to solution of the Euler ones, producing weak solutions which are energy conserving.</p>","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139918622","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
Multiplicity and concentration of solutions for a Choquard equation with critical exponential growth in $$mathbb {R}^N$$ 在 $$mathbb {R}^N$ 中具有临界指数增长的 Choquard 方程的解的多重性和浓度
Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-02-19 DOI: 10.1007/s00030-023-00916-1
Shengbing Deng, Xingliang Tian, Sihui Xiong
{"title":"Multiplicity and concentration of solutions for a Choquard equation with critical exponential growth in $$mathbb {R}^N$$","authors":"Shengbing Deng, Xingliang Tian, Sihui Xiong","doi":"10.1007/s00030-023-00916-1","DOIUrl":"https://doi.org/10.1007/s00030-023-00916-1","url":null,"abstract":"<p>In this paper, we consider the following Choquard equation </p><span>$$begin{aligned} -varepsilon ^{N}Delta _{N}u+V(x)|u|^{N-2}u=varepsilon ^{mu -N}left( I_mu *F(u)right) f(u) quad {text{ in }quad mathbb {R}^N}, end{aligned}$$</span><p>where <span>(Nge 3)</span>, <span>(I_mu =|x|^{-mu })</span> with <span>(0&lt;mu &lt;N)</span>, <span>(Delta _{N}u=textrm{div}(|nabla u|^{N-2}nabla u))</span> denotes the <i>N</i>-Laplacian operator, <i>V</i>(<i>x</i>) is a continuous real function on <span>(mathbb {R}^N)</span>, <i>F</i>(<i>s</i>) is the primitive of <i>f</i>(<i>s</i>) and <span>(varepsilon )</span> is a positive parameter. Assuming that the nonlinearity <i>f</i>(<i>s</i>) has critical exponential growth in the sense of Trudinger–Moser inequality, we establish the existence, multiplicity and concentration of solutions by variational methods and Ljusternik–Schnirelmann theory, which extends the works of Alves and Figueiredo (J Differ Equ 246:1288–1311, 2009) to the problem with Choquard nonlinearity, Alves et al. (J Differ Equ 261:1933–1972, 2016) to higher dimension.</p>","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139918565","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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