Nonlinear Analysis-Real World Applications最新文献

{"title":"Persistence and zero-Hopf equilibrium in the tritrophic food chain model with Holling functional response","authors":"Víctor Castellanos ,&nbsp;Jaume Llibre","doi":"10.1016/j.nonrwa.2024.104232","DOIUrl":"10.1016/j.nonrwa.2024.104232","url":null,"abstract":"<div><div>In this paper, we analyze the persistence of three species in a three-level food chain model. We characterize when such a model exhibits a zero-Hopf equilibrium point and show that it is possible only if the functional responses in the model are of type Holling III or IV.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142535940","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":"Effects of marine reserve creation in single species and prey–predator models","authors":"Aleksander Ćwiszewski ,&nbsp;Sławomir Plaskacz","doi":"10.1016/j.nonrwa.2024.104230","DOIUrl":"10.1016/j.nonrwa.2024.104230","url":null,"abstract":"<div><div>Implementations of marine protected areas (MPA’s) for over-exploited single species fisheries and prey–predator models with environment capacity are studied. The situations when fishing effort reaches the extinction threshold that fits over-exploited open-access fisheries are considered. The discrepancy for single-species and prey–predator models in the context of food security is obtained. Due quantitative indicators for biodiversity and food security are introduced and analyzed.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142423047","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A simple proof of uniqueness for the nonlocal positive solutions","authors":"Ming-Ming Fan,&nbsp;Jian-Wen Sun","doi":"10.1016/j.nonrwa.2024.104233","DOIUrl":"10.1016/j.nonrwa.2024.104233","url":null,"abstract":"<div><div>In this paper, we prove a general uniqueness result for the positive solution of nonlocal dispersal equations. Our simple and elementary proof simplifies previously known proofs based on eigenvalue theory and solution estimates.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142423046","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":"Dynamic bifurcation of nonautonomous evolution equations under Landesman–Lazer condition with cohomology methods","authors":"Chunqiu Li,&nbsp;Jintao Wang","doi":"10.1016/j.nonrwa.2024.104228","DOIUrl":"10.1016/j.nonrwa.2024.104228","url":null,"abstract":"<div><div>In this article we study the dynamic bifurcation of nonautonomous evolution equations by using cohomology methods. First, we construct a homotopy equivalence relation between the nonautonomous system and a product flow. Then, we slightly extend some continuation theorems on bifurcations for autonomous equations, and prove some new cohomology consequences on the reduced singular groups. Based on this homotopy equivalence relation and these conclusions, we establish some typical results on the dynamic bifurcation from infinity of the abstract nonautonomous evolution equation. Finally, we consider the parabolic equation <span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>=</mo><mi>λ</mi><mi>u</mi><mo>+</mo><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>)</mo></mrow><mo>+</mo><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span> associated with the Dirichlet boundary condition, where <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>u</mi><mo>)</mo></mrow></mrow></math></span> satisfies the appropriate Landesman–Lazer type condition. Some new results on the dynamical behaviors of this equation near resonance of the equation are derived.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142423045","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":"Local Lipschitz continuity for energy integrals with slow growth and lower order terms","authors":"Michela Eleuteri ,&nbsp;Stefania Perrotta ,&nbsp;Giulia Treu","doi":"10.1016/j.nonrwa.2024.104224","DOIUrl":"10.1016/j.nonrwa.2024.104224","url":null,"abstract":"<div><div>We consider integral functionals with slow growth and explicit dependence on <span><math><mi>u</mi></math></span> of the Lagrangian; this includes many relevant examples as, for instance, in elastoplastic torsion problems or in image restoration problems. Our aim is to prove that the local minimizers are locally Lipschitz continuous. The proof makes use of recent results concerning the Bounded Slope Conditions.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142423020","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"New generalization of non-autonomous Bernfeld–Haddock conjecture and its proof","authors":"Chuangxia Huang ,&nbsp;Xiaodan Ding","doi":"10.1016/j.nonrwa.2024.104226","DOIUrl":"10.1016/j.nonrwa.2024.104226","url":null,"abstract":"<div><div>In this paper, the famous Bernfeld–Haddock conjecture is generalized to a broader form combining with a class of non-autonomous delay differential equations. With the help of differential inequality technique and Dini derivative theory, it is proved that each solution of the addressed equations has boundedness and tends to a constant without requiring the delay feedback function to be strictly increasing, which greatly refines and extends the corresponding results in the existing literature. In particular, an explanatory example is performed to substantiate the obtained analytical findings.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142359400","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":"Bifurcation and dynamics of periodic solutions of MEMS model with squeeze film damping","authors":"Shiping Lu ,&nbsp;Xingchen Yu ,&nbsp;Zhuomo An","doi":"10.1016/j.nonrwa.2024.104229","DOIUrl":"10.1016/j.nonrwa.2024.104229","url":null,"abstract":"&lt;div&gt;&lt;div&gt;In this paper, we study the oscillations of an idealized mass–spring model of micro-electro-mechanical system (MEMS) with squeeze film damping. The model consists of two parallel electrodes separated by a gap &lt;span&gt;&lt;math&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;: one of them is fixed, and another one is movable and attached to a linear spring with stiffness coefficient &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. The oscillation, under the influence of AC–DC voltage &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;cos&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;π&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, is ruled by the following singular differential equation &lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;′&lt;/mo&gt;&lt;mo&gt;′&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;′&lt;/mo&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;V&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;.&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;Here, &lt;span&gt;&lt;math&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; is the vertical displacement of the moving plate (&lt;span&gt;&lt;math&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; is always assumed to be less than &lt;span&gt;&lt;math&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;), &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; is its mass, &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; is the electrode area, and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;θ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; is the absolute dielectric constant of vacuum. Taking &lt;span&gt;&lt;math&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; as the parameter, we show the existence of saddle–node bifurcation of &lt;span&gt;&lt;math&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;-periodic solutions to the equation in the parameter space. This answers, from certain point of view, the open problem proposed by Torres in his monograph, see Torres (2015, Open Problem 2.1, p. 18). Further, we prove that the equation has exactly two classes of &lt;span&gt;&lt;math&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;-periodic solutions: as &lt;span&gt;&lt;math&gt;&lt;mi&gt;d&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; tends to &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;∞&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, one of them uniformly tends t","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142328262","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 planar equation involving (2,q)-Laplacian with zero mass and Trudinger–Moser nonlinearity","authors":"J.A. Cardoso ,&nbsp;J.C. de Albuquerque ,&nbsp;J. Carvalho ,&nbsp;G.M. Figueiredo","doi":"10.1016/j.nonrwa.2024.104227","DOIUrl":"10.1016/j.nonrwa.2024.104227","url":null,"abstract":"<div><div>In this work, we study existence of positive solutions to a class of <span><math><mrow><mo>(</mo><mn>2</mn><mo>,</mo><mi>q</mi><mo>)</mo></mrow></math></span>-equations in the zero mass case in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>. We establish a weighted Sobolev embedding and we introduce a new Trudinger–Moser type inequality. Moreover, since we work on a suitable radial Sobolev space, we prove an appropriate version of the well-known Symmetric Criticality Principle by Palais. Finally, we study regularity of solutions applying Moser iteration scheme.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142318795","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":"Singular non-autonomous (p,q)-equations with competing nonlinearities","authors":"Nikolaos S. Papageorgiou ,&nbsp;Dongdong Qin ,&nbsp;Vicenţiu D. Rădulescu","doi":"10.1016/j.nonrwa.2024.104225","DOIUrl":"10.1016/j.nonrwa.2024.104225","url":null,"abstract":"<div><div>We consider a parametric non-autonomous <span><math><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></math></span>-equation with a singular term and competing nonlinearities, a parametric concave term and a Carathéodory perturbation. We consider the cases where the perturbation is <span><math><mrow><mo>(</mo><mi>p</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></math></span>-linear and where it is <span><math><mrow><mo>(</mo><mi>p</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></math></span>-superlinear (but without the use of the Ambrosetti–Rabinowitz condition). We prove an existence and multiplicity result which is global in the parameter <span><math><mrow><mi>λ</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span> (a bifurcation type result). Also, we show the existence of a smallest positive solution and show that it is strictly increasing as a function of the parameter. Finally, we examine the set of positive solutions as a function of the parameter (solution multifunction). First, we show that the solution set is compact in <span><math><mrow><msubsup><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>1</mn></mrow></msubsup><mrow><mo>(</mo><mover><mrow><mi>Ω</mi></mrow><mrow><mo>̄</mo></mrow></mover><mo>)</mo></mrow></mrow></math></span> and then we show that the solution multifunction is Vietoris continuous and also Hausdorff continuous as a multifunction of the parameter.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142311429","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 inertial manifolds for semilinear parabolic equations under Lipschitz perturbations","authors":"Jihoon Lee ,&nbsp;Thanhnguyen Nguyen","doi":"10.1016/j.nonrwa.2024.104219","DOIUrl":"10.1016/j.nonrwa.2024.104219","url":null,"abstract":"<div><div>In this paper we study the stability and continuity of inertial manifolds for semilinear parabolic equations. More precisely, we prove the continuity of inertial manifolds and the Gromov–Hausdorff stability of dynamical systems on inertial manifolds for reaction diffusion equations under Lipschitz perturbations of the domain and equation, using a nontrivial generalization of ODE approach discussed in Romanov (1994).</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142311428","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}