Journal of Differential Equations最新文献

{"title":"Structural stability of smooth axisymmetric subsonic spiral flows with self-gravitation in a concentric cylinder","authors":"Chunpeng Wang,&nbsp;Zihao Zhang","doi":"10.1016/j.jde.2025.113356","DOIUrl":"10.1016/j.jde.2025.113356","url":null,"abstract":"<div><div>This paper concerns the existence and stability of smooth axisymmetric subsonic spiral flows with self-gravitation in a concentric cylinder. Firstly, the existence and uniqueness of smooth cylindrically symmetric subsonic spiral flows with self-gravitation are proved. Then we establish the structural stability of this background subsonic flows under axisymmetric perturbations of suitable boundary conditions, which yields the existence and uniqueness of smooth axisymmetric subsonic spiral flows with nonzero angular velocity and vorticity to the steady self-gravitating Euler-Poisson system. By the stream function formulation, the steady Euler-Poisson system for the axisymmetric self-gravitating flows can be decomposed into a second-order nonlinear elliptic system coupled with several transport equations. The key ingredient of the analysis is to discover a special structure of the associated elliptic system for the stream function and the gravitational potential, which enable us to obtain a priori estimates for the linearized elliptic problem.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"438 ","pages":"Article 113356"},"PeriodicalIF":2.4,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143870201","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The initial value problem of the fractional compressible Navier-Stokes-Poisson system","authors":"Shu Wang,&nbsp;Shuzhen Zhang","doi":"10.1016/j.jde.2025.113359","DOIUrl":"10.1016/j.jde.2025.113359","url":null,"abstract":"<div><div>We consider the initial value problem to the fractional generalized compressible Navier-Stokes-Poisson equations for viscous fluids with one Levy diffusion process in which the viscosity term appeared in the fluid equations and the diffusion term for the internal electrostatic potential are described respectively by the nonlocal fractional Laplace operators. The global-in-time existence of the smooth solution is proven under the assumption that the initial data are given in a small neighborhood of a constant state in the sense of Sobolev's space. The optimal decay rates depending upon the orders of two fractional Laplace operators are established, and that the momentum of the fractional Navier-Stokes-Poisson system exhibits a slower convergence rate in time to the constant state compared to that of the fractional compressible Navier-Stokes system is also shown.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"438 ","pages":"Article 113359"},"PeriodicalIF":2.4,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143873891","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Existence and stability of positive solutions in a parabolic problem with a nonlinear incoming flux on the boundary","authors":"Shangjiang Guo","doi":"10.1016/j.jde.2025.113349","DOIUrl":"10.1016/j.jde.2025.113349","url":null,"abstract":"<div><div>In this paper, we consider a parabolic problem with a nonlinear boundary condition which is induced by the incoming flux on the boundary. We focus on analyzing the existence and stability of bifurcating positive solutions emanating from trivial solutions. Our approach combines the Lyapunov-Schmidt method with classical local bifurcation theory, extending the framework established by Crandall and Rabinowitz. The results provide new insights into the structure and stability properties of solutions under nonlinear flux boundary effects.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"436 ","pages":"Article 113349"},"PeriodicalIF":2.4,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143868174","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On conservative solutions to the generalized hyperelastic-rod equation","authors":"Yu Gao","doi":"10.1016/j.jde.2025.113355","DOIUrl":"10.1016/j.jde.2025.113355","url":null,"abstract":"<div><div>This paper investigates a generalized hyperelastic-rod wave equation within its generalized framework. For conservative solutions, we establish that the singularities of the energy measure can only occur at countably many times. Furthermore, we prove the uniqueness of the solution by employing a refined characteristics method.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"438 ","pages":"Article 113355"},"PeriodicalIF":2.4,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143870197","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Type II singularities in area-preserving curvature flows of convex symmetric immersed closed plane curves","authors":"Koichi Anada ,&nbsp;Tetsuya Ishiwata ,&nbsp;Takeo Ushijima","doi":"10.1016/j.jde.2025.113348","DOIUrl":"10.1016/j.jde.2025.113348","url":null,"abstract":"<div><div>We deal with the area-preserving curvature flow in the plane, particularly the blow-up phenomena of curvatures on cusp singularities in contractions of convex immersed curves with self-crossing points. For Abresch-Langer type curves with highly symmetric properties, it has been known that the maximum of curvatures blows up at a finite time under some assumptions. In this paper, we consider the blow-up rates in this case.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"437 ","pages":"Article 113348"},"PeriodicalIF":2.4,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143869741","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the borderline regularity criterion in anisotropic Lebesgue spaces of the Navier-Stokes equations","authors":"Yanqing Wang ,&nbsp;Wei Wei ,&nbsp;Gang Wu ,&nbsp;Daoguo Zhou","doi":"10.1016/j.jde.2025.113351","DOIUrl":"10.1016/j.jde.2025.113351","url":null,"abstract":"<div><div>In this paper, we are concerned with the critical mixed norm regularity of Leray-Hopf weak solutions of the Navier-Stokes equations in three dimensions and higher dimensions. It is shown that <span><math><mi>u</mi><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>(</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>;</mo><msup><mrow><mi>L</mi></mrow><mrow><mover><mrow><mi>q</mi></mrow><mrow><mo>→</mo></mrow></mover></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo><mo>)</mo></math></span> with <span><math><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>n</mi></mrow></munderover><mfrac><mrow><mn>1</mn></mrow><mrow><msub><mrow><mi>q</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></mfrac><mo>=</mo><mn>1</mn></math></span> ensure that Leray-Hopf weak solutions are regular. A new ingredient is <em>ε</em>-regularity criterion derived by the De Giorgi iteration technique under this critical regularity in high spatial dimension.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"438 ","pages":"Article 113351"},"PeriodicalIF":2.4,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143870203","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Expansion coefficients and their relation for Melnikov functions near polycycles","authors":"Feng Liang ,&nbsp;Maoan Han","doi":"10.1016/j.jde.2025.113312","DOIUrl":"10.1016/j.jde.2025.113312","url":null,"abstract":"<div><div>Under a suitable assumption we obtain some new results on expansion coefficients and their relation for the first order Melnikov functions near any <em>m</em>-polycycle with hyperbolic saddles, <span><math><mi>m</mi><mo>∈</mo><msup><mrow><mi>N</mi></mrow><mrow><mo>+</mo></mrow></msup></math></span>, which establish a general bifurcation theory on limit cycles near the <em>m</em>-polycycles. As an application we consider 2-polycyclic bifurcations for a <em>φ</em>-Laplacian Liénard system and gain the number of limit cycles near the polycycle with two hyperbolic saddles.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"435 ","pages":"Article 113312"},"PeriodicalIF":2.4,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143869155","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On determination of the bifurcation type for a free boundary problem modeling tumor growth","authors":"Xinyue Evelyn Zhao ,&nbsp;Junping Shi","doi":"10.1016/j.jde.2025.113352","DOIUrl":"10.1016/j.jde.2025.113352","url":null,"abstract":"<div><div>Many mathematical models in different disciplines involve the formulation of free boundary problems, where the domain boundaries are not predefined. These models present unique challenges, notably the nonlinear coupling between the solution and the boundary, which complicates the identification of bifurcation types. This paper mainly investigates the structure of symmetry-breaking bifurcations in a two-dimensional free boundary problem modeling tumor growth. By expanding the solution to a high order with respect to a small parameter and computing the bifurcation direction at each bifurcation point, we demonstrate that all the symmetry-breaking bifurcations occurred in the model, as established by the Crandall-Rabinowitz Bifurcation From Simple Eigenvalue Theorem, are pitchfork bifurcations. These findings reveal distinct behaviors between the two-dimensional and three-dimensional cases of the same model.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"436 ","pages":"Article 113352"},"PeriodicalIF":2.4,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143868175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Asymptotics for quasilinear wave equations in exterior domains","authors":"Weimin Peng ,&nbsp;Dongbing Zha","doi":"10.1016/j.jde.2025.113353","DOIUrl":"10.1016/j.jde.2025.113353","url":null,"abstract":"<div><div>The main concern of this paper is the asymptotic behavior of global classical solution to exterior domain problem for three-dimensional quasilinear wave equations satisfying null condition, in the small data setting. For this purpose, we first provide an alternative proof for the global existence result via purely energy approach, in which only the general derivatives and spatial rotation operators are employed as commuting vector fields. Then based on this new proof, we show that the global solution will scatter, that is, it will converge to some solution of homogeneous linear wave equations, in the energy sense, as time tends to infinity. We also show that the global solution can be determined by the scattering data uniquely, i.e., the inverse scattering property holds.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"437 ","pages":"Article 113353"},"PeriodicalIF":2.4,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143869742","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Reverse Faber-Krahn and Szegő-Weinberger type inequalities for annular domains under Robin-Neumann boundary conditions","authors":"T.V. Anoop ,&nbsp;Vladimir Bobkov ,&nbsp;Pavel Drábek","doi":"10.1016/j.jde.2025.113354","DOIUrl":"10.1016/j.jde.2025.113354","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Let &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;τ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; be the &lt;em&gt;k&lt;/em&gt;-th eigenvalue of the Laplace operator in a bounded domain Ω of the form &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mtext&gt;out&lt;/mtext&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;∖&lt;/mo&gt;&lt;mover&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;mo&gt;‾&lt;/mo&gt;&lt;/mover&gt;&lt;/math&gt;&lt;/span&gt; under the Neumann boundary condition on &lt;span&gt;&lt;math&gt;&lt;mo&gt;∂&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mtext&gt;out&lt;/mtext&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; and the Robin boundary condition with parameter &lt;span&gt;&lt;math&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; on the sphere &lt;span&gt;&lt;math&gt;&lt;mo&gt;∂&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; of radius &lt;span&gt;&lt;math&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; centered at the origin, the limiting case &lt;span&gt;&lt;math&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; being understood as the Dirichlet boundary condition on &lt;span&gt;&lt;math&gt;&lt;mo&gt;∂&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;. In the case &lt;span&gt;&lt;math&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;, it is known that the first eigenvalue &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;τ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; does not exceed &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;τ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;∖&lt;/mo&gt;&lt;mover&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;mo&gt;‾&lt;/mo&gt;&lt;/mover&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, where &lt;span&gt;&lt;math&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; is chosen such that &lt;span&gt;&lt;math&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;∖&lt;/mo&gt;&lt;mover&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;mo&gt;‾&lt;/mo&gt;&lt;/mover&gt;&lt;mo&gt;|&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;, which can be regarded as a reverse Faber-Krahn type inequality. We establish this result for any &lt;span&gt;&lt;math&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mo&gt;∞&lt;/mo&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. Moreover, we provide related estimates for higher eigenvalues under additional geometric assumptions on Ω, which can be seen as Szegő-Weinberger type inequalities. A few counterexamples to the obtained inequalities for domains violating imposed geometric assumptions are given. As auxiliary information, we investigate shapes of eigenfunctions associated with several eigenvalues &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;τ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;∖&lt;/mo&gt;&lt;mover&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;mo&gt;‾&lt;/mo&gt;&lt;/mover&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; and show that they are nonradial at least for all positive and all sufficiently negative &lt;em&gt;h&lt;/em&gt; when ","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"437 ","pages":"Article 113354"},"PeriodicalIF":2.4,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143869743","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}