Nonlinear Analysis-Real World Applications最新文献

{"title":"Integrability and periodic orbits of a 3D jerk system with two quadratic nonlinearities","authors":"Martha Alvarez-Ramírez ,&nbsp;Johanna D. García-Saldaña ,&nbsp;Jaume Llibre","doi":"10.1016/j.nonrwa.2025.104491","DOIUrl":"10.1016/j.nonrwa.2025.104491","url":null,"abstract":"<div><div>In mechanics jerk is the rate of change of an object’s acceleration over time. Thus a jerk equation is a differential equation of the form <span><math><mrow><mover><mrow><mi>x</mi></mrow><mrow><mo>⃛</mo></mrow></mover><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mover><mrow><mi>x</mi></mrow><mrow><mo>̇</mo></mrow></mover><mo>,</mo><mover><mrow><mi>x</mi></mrow><mrow><mo>̈</mo></mrow></mover><mo>)</mo></mrow></mrow></math></span>, where <span><math><mi>x</mi></math></span>, <span><math><mover><mrow><mi>x</mi></mrow><mrow><mo>̇</mo></mrow></mover></math></span>, <span><math><mover><mrow><mi>x</mi></mrow><mrow><mo>̈</mo></mrow></mover></math></span> and <span><math><mover><mrow><mi>x</mi></mrow><mrow><mo>⃛</mo></mrow></mover></math></span> represent the position, velocity, acceleration, and jerk, respectively. The jerk differential equation can be written as the jerk differential system <span><math><mrow><mover><mrow><mi>x</mi></mrow><mrow><mo>̇</mo></mrow></mover><mo>=</mo><mi>y</mi><mo>,</mo><mspace></mspace><mover><mrow><mi>y</mi></mrow><mrow><mo>̇</mo></mrow></mover><mo>=</mo><mi>z</mi><mo>,</mo><mspace></mspace><mover><mrow><mi>z</mi></mrow><mrow><mo>̇</mo></mrow></mover><mo>=</mo><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>)</mo></mrow><mo>,</mo></mrow></math></span> in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. In this paper we study the jerk differential system with <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>,</mo><mi>z</mi><mo>)</mo></mrow><mo>=</mo><mo>−</mo><mi>a</mi><mi>x</mi><mrow><mo>(</mo><mn>1</mn><mo>−</mo><mi>x</mi><mo>)</mo></mrow><mo>−</mo><mi>y</mi><mo>+</mo><mi>b</mi><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math></span>, previously studied by other authors showing that this system can exhibit chaos for some values of its parameters. When the parameters <span><math><mrow><mi>a</mi><mo>=</mo><mi>b</mi><mo>=</mo><mn>0</mn></mrow></math></span> the <span><math><mi>x</mi></math></span>-axis is filled with zero-Hopf equilibria, and all the other orbits are periodic. Here we prove analytically the existence of two families of periodic orbits for sufficiently small values of the parameters <span><math><mi>a</mi></math></span> and <span><math><mi>b</mi></math></span>. One family bifurcates from the non-isolated zero-Hopf equilibrium <span><math><mrow><mo>(</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></math></span> of the jerk system with <span><math><mrow><mi>a</mi><mo>=</mo><mi>b</mi><mo>=</mo><mn>0</mn></mrow></math></span>, while the other family bifurcates from a periodic orbit of the jerk system with <span><math><mrow><mi>a</mi><mo>=</mo><mi>b</mi><mo>=</mo><mn>0</mn></mrow></math></span>.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104491"},"PeriodicalIF":1.8,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144932266","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On a fractional boundary version of Talenti’s inequality in the unit ball","authors":"Yassin El Karrouchi,&nbsp;Tobias Weth","doi":"10.1016/j.nonrwa.2025.104482","DOIUrl":"10.1016/j.nonrwa.2025.104482","url":null,"abstract":"<div><div>Inspired by recent work of Ferone and Volzone (2021), we derive sufficient conditions for the validity and non-validity of a boundary version of Talenti’s comparison principle in the context of Dirichlet–Poisson problems for the fractional Laplacian <span><math><msup><mrow><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow></mrow><mrow><mi>s</mi></mrow></msup></math></span> in the unit ball <span><math><mrow><mi>Ω</mi><mo>=</mo><msub><mrow><mi>B</mi></mrow><mrow><mn>1</mn></mrow></msub><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></mrow></math></span>, <span><math><mrow><mi>s</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>. In particular, our results imply a universal failure of the classical pointwise Talenti inequality in the fractional radial context. In contrast, a boundary Talenti type inequality holds for radial functions in the higher order case <span><math><mrow><mi>s</mi><mo>&gt;</mo><mn>1</mn></mrow></math></span>.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104482"},"PeriodicalIF":1.8,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144932349","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stability of the Prandtl boundary layer equation under various boundary conditions","authors":"Huashui Zhan","doi":"10.1016/j.nonrwa.2025.104490","DOIUrl":"10.1016/j.nonrwa.2025.104490","url":null,"abstract":"<div><div>By the Crocco transformation, the boundary layer system of the viscous incompressible flow is transferred to a strong degenerate parabolic equation with a nonlinear boundary value condition, referred as the Prandtl boundary layer equation. The key technique in this paper involves applying the reciprocal transformation to convert the Prandtl boundary layer equation into a degenerate parabolic equation in divergent form. The main challenge arises on account of that the reciprocal transformation renders the initial value condition unbounded. To address this, a new unknown function <span><math><msub><mrow><mi>u</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> is introduced, and the partial differential equation for <span><math><msub><mrow><mi>u</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> is derived. For this new equation, the existence of these BV entropy solutions are proved by the parabolically regularized method, the maximal value principle is used to obtain the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup></math></span>-estimate. Under certain restrictions on the data of the Prandtl system, the stability of entropy solutions is demonstrated using different boundary value conditions. Consequently, under the Oleǐnik assumption and the monotonicity condition, the two-dimensional Prandtl boundary layer system is shown to be well-posed through the inverse Crocco transformation.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104490"},"PeriodicalIF":1.8,"publicationDate":"2025-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144921984","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Persistence of harmful algal blooms under conditions of internal phosphorus loading","authors":"Felipe Breton ,&nbsp;Carlos Martínez","doi":"10.1016/j.nonrwa.2025.104479","DOIUrl":"10.1016/j.nonrwa.2025.104479","url":null,"abstract":"<div><div>Phosphorus release from sediments in lakes can trigger harmful algal blooms, significantly impacting lake ecosystems and necessitating effective management strategies. This study presents a mathematical analysis of a dynamic model incorporating such internal phosphorus loadings and their impact on algal growth. The model accounts for both light and phosphorus limitations on cell growth, as well as the seasonal variability of temperature and light, leading to a periodically forced non-linear system of ordinary differential equations. Using the theory of periodic semiflows and Floquet multipliers, we establish both necessary and sufficient conditions for long-term survival of algae (uniform persistence). This approach provides a threshold result for algae survival and the existence of a non-trivial periodic solution. Through numerical simulations, we illustrate our results and provide insights into the role of internal phosphorus loadings. In particular, our simulations illustrate that an integrated strategy reducing both watershed inflows and sediment phosphorus outperforms measures that focus on just one source of phosphorus.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104479"},"PeriodicalIF":1.8,"publicationDate":"2025-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144865885","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global solutions to the angiogenesis system with p-Laplacian diffusion","authors":"Changchun Liu,&nbsp;Yue Zhou","doi":"10.1016/j.nonrwa.2025.104478","DOIUrl":"10.1016/j.nonrwa.2025.104478","url":null,"abstract":"<div><div>In this paper, we consider a angiogenesis system with <span><math><mi>p</mi></math></span>-Laplacian diffusion <span><span><span><math><mfenced><mrow><mtable><mtr><mtd><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mo>∇</mo><mi>⋅</mi><mfenced><mrow><mrow><mo>(</mo><msup><mrow><mfenced><mrow><mo>∇</mo><mi>u</mi></mrow></mfenced></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow></msup><mo>+</mo><mi>δ</mi><mo>)</mo></mrow><mo>∇</mo><mi>u</mi></mrow></mfenced><mo>−</mo><mi>χ</mi><mo>∇</mo><mi>⋅</mi><mfenced><mrow><mi>u</mi><mo>∇</mo><mi>v</mi></mrow></mfenced><mo>,</mo><mspace></mspace><mspace></mspace><mspace></mspace></mtd><mtd><mspace></mspace><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo><mspace></mspace><mi>t</mi><mo>&gt;</mo><mn>0</mn><mo>,</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mo>−</mo><mi>u</mi><mi>v</mi><mo>,</mo><mspace></mspace><mspace></mspace><mspace></mspace></mtd><mtd><mspace></mspace><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo><mspace></mspace><mi>t</mi><mo>&gt;</mo><mn>0</mn><mo>,</mo></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>in a bounded domain <span><math><mrow><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mrow><mo>(</mo><mi>N</mi><mo>≥</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span> with smooth boundary. For all <span><span><span><math><mrow><mi>p</mi><mo>&gt;</mo><msub><mrow><mi>p</mi></mrow><mrow><mo>∗</mo></mrow></msub><mo>=</mo><mo>max</mo><mrow><mo>{</mo><mn>2</mn><mo>,</mo><mfrac><mrow><mn>1</mn><mo>+</mo><msqrt><mrow><mn>1</mn><mo>+</mo><mn>4</mn><mi>N</mi></mrow></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac><mo>}</mo></mrow><mo>,</mo></mrow></math></span></span></span>we prove the existence of global strong solution.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104478"},"PeriodicalIF":1.8,"publicationDate":"2025-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144858431","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Symmetry breaking for nonhomogeneous Hénon-type problems involving the 1-Laplacian operator","authors":"Marcos T.O. Pimenta ,&nbsp;Yino B. Cueva Carranza ,&nbsp;Giovany M. Figueiredo ,&nbsp;Olimpio Hiroshi Miyagaki","doi":"10.1016/j.nonrwa.2025.104480","DOIUrl":"10.1016/j.nonrwa.2025.104480","url":null,"abstract":"<div><div>In this paper we study the nonhomogeneous Hénon elliptic problem involving the 1-Laplacian operator within the unit ball. Under some assumptions on the nonlinearity, and for sufficiently large parameter values, we establish the existence of a non-radial solution. Our approach relies on an approximation scheme in which the solution is obtained as the limit of solutions to <span><math><mi>p</mi></math></span>-Laplacian type problems.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104480"},"PeriodicalIF":1.8,"publicationDate":"2025-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144852257","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global strong solutions to the 3D nonhomogeneous incompressible magneto-micropolar fluid equations with density-dependent viscosity","authors":"Xia Ye ,&nbsp;Yue Zhou ,&nbsp;Mingxuan Zhu","doi":"10.1016/j.nonrwa.2025.104477","DOIUrl":"10.1016/j.nonrwa.2025.104477","url":null,"abstract":"<div><div>This paper concerns the Cauchy problem for magneto-micropolar fluid equations with density-dependent viscosity in the entire space <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. By utilizing some crucial decay-in-time estimates, we establish the global existence and uniqueness of strong solutions, provided that the initial velocity is suitably small, without requiring smallness of the initial density.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104477"},"PeriodicalIF":1.8,"publicationDate":"2025-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144830107","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A competitive chemostat model with time-dependent delays","authors":"Teresa Faria ,&nbsp;Jaqueline G. Mesquita","doi":"10.1016/j.nonrwa.2025.104476","DOIUrl":"10.1016/j.nonrwa.2025.104476","url":null,"abstract":"<div><div>A non-autonomous chemostat model with time-dependent delays modelling <span><math><mi>n</mi></math></span> microorganisms in competition is derived and studied. Under very mild general conditions on the coefficients and time-varying delays, we study the extinction of all the species and, in the case of a periodic system, the existence of nontrivial and nonnegative periodic solutions. For the model with a simple microorganism, a criterion for the uniform persistence is established, which also implies the global attractivity of any positive solution. In this way, a criterion for the existence, uniqueness and global attractivity of a positive periodic solution is derived. These results largely generalise and enhance recent achievements in the literature.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104476"},"PeriodicalIF":1.8,"publicationDate":"2025-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144830106","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global stabilization and regulation of prey immigration for predator–prey models","authors":"Jitsuro Sugié","doi":"10.1016/j.nonrwa.2025.104468","DOIUrl":"10.1016/j.nonrwa.2025.104468","url":null,"abstract":"<div><div>Observations of predator–prey dynamics in nature often reveal varying predation rates at different prey densities. However, the stabilizing or regulatory influence of constant prey immigration in predator–prey models incorporating a Holling type III functional response remains unclear. This study aims to address this issue by examining prey immigration as a stabilizing and regulating mechanism in ecosystems. This is achieved by employing a predator–prey model, with the predation process represented by a functional response involving Holling type III. The model admits at most one interior equilibrium point. A mathematical formulation is used to establish the interplay between the destabilization of the interior equilibrium point owing to increased carrying capacity and stabilization arising from constant prey immigration. Under certain conditions, an increase in carrying capacity disrupts the previously stable interior equilibrium point, resulting in the emergence of a stable limit cycle. The amplitude of this limit cycles grows as the carrying capacity increases, heightening the risk of ecosystem extinction. Conversely, constant prey immigration attenuates the destabilization of the interior equilibrium point and mitigates the amplification of the limit cycle. Necessary and sufficient conditions for global asymptotic stability of the interior equilibrium point and uniqueness of limit cycles are derived by transforming the model into a Liénard-type system with multiple parameters to validate these findings. The study findings enable the formulation of the effects of constant prey immigration on the stabilization and regulation in predator–prey models.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104468"},"PeriodicalIF":1.8,"publicationDate":"2025-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144830096","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the justification of Koiter’s model for elliptic membrane shells subjected to an interior normal unilateral contact condition","authors":"Paolo Piersanti","doi":"10.1016/j.nonrwa.2025.104473","DOIUrl":"10.1016/j.nonrwa.2025.104473","url":null,"abstract":"<div><div>The purpose of this paper is twofold. First, we rigorously justify Koiter’s model for linearly elastic elliptic membrane shells in the case where the shell is subject to a geometrical constraint modelled via an interior normal unilateral contact condition defined in the interior of the shell. To achieve this, we establish a novel density result for non-empty, closed, and convex subsets of Lebesgue spaces, which are applicable to cases not covered by the “density property” established in Ciarlet et al. (2019).</div><div>Second, we demonstrate that the solution to the two-dimensional obstacle problem for linearly elastic elliptic membrane shells, subjected to the interior normal unilateral contact condition, exhibits higher regularity throughout its entire definition domain. A key feature of this result is that, while the transverse component of the solution is, in general, only of class <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and its trace is <em>a priori</em> undefined, the methodology proposed here, partially based on Ciarlet and Sanchez-Palencia (1996), enables us to rigorously establish the well-posedness of the trace for the transverse component of the solution by means of an <em>ad hoc</em> formula.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"88 ","pages":"Article 104473"},"PeriodicalIF":1.8,"publicationDate":"2025-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144830097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}