Nonlinear Analysis-Real World Applications最新文献

{"title":"Asymptotic analysis for an age-structured predator–prey model with Beddington–Deangelis functional response","authors":"Yuan Yuan ,&nbsp;Xianlong Fu","doi":"10.1016/j.nonrwa.2025.104345","DOIUrl":"10.1016/j.nonrwa.2025.104345","url":null,"abstract":"<div><div>This paper focuses on the asymptotic behavior of an age-structured predator–prey model with Beddington–Deangelis functional response and two delays. The model is first formulated as an abstract non-densely defined Cauchy problem and the existence of the equilibria is obtained under some conditions. Then, the global asymptotic stability of the boundary equilibrium is successfully established by determining the distribution of eigenvalues. Hopf bifurcation results with two parameters are also well described under some conditions by the method of stability switching curves. Finally, some numerical examples are presented to further deepen the understanding of the obtained results.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104345"},"PeriodicalIF":1.8,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143519518","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 behavior of an extended Gao beam model including shear deformation","authors":"Bartłomiej Dyniewicz ,&nbsp;Meir Shillor ,&nbsp;Czesław I. Bajer","doi":"10.1016/j.nonrwa.2025.104340","DOIUrl":"10.1016/j.nonrwa.2025.104340","url":null,"abstract":"<div><div>This study develops a model of the dynamics of the extended 2D Gao beam and simulates it. Here, the static model studied by Dyniewicz, Shillor and Bajer (Meccanica, 2024), is modified by incorporating inertial terms to account for dynamic behavior. The beam model expands the 1D Gao beam, which can oscillate around a buckled position, and the Timoshenko beam, which factors in shear effects in the beam’s cross sections. The resulting model consists of two highly nonlinear wave equations, alongside specified initial and boundary conditions. A finite element method (FEM) algorithm is created and executed to analyze the system’s vibrations induced by a periodically oscillating longitudinal compressive force. The simulation results are discussed, highlighting the ways the initial conditions influence the solutions, which are graphically illustrated through phase portraits. From an engineering viewpoint, this thick Gao beam model is notable for its relative simplicity. Similarly to the Timoshenko beam model, it includes shear effects, yielding a wave-like equation of motion. Considerations of the shear are essential for accurately analyzing thicker beams, as traditional models that overlook them may fail to capture the true system behaviors. Consequently, this extended Gao model offers more realistic outcomes in dynamic scenarios.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104340"},"PeriodicalIF":1.8,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143474959","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 existence in a three-dimensional chemotaxis-Stokes system with p-Laplacian diffusion and singular sensitivity","authors":"Ruina He,&nbsp;Zhongping Li","doi":"10.1016/j.nonrwa.2025.104339","DOIUrl":"10.1016/j.nonrwa.2025.104339","url":null,"abstract":"<div><div>This paper considers the following chemotaxis-Stokes system <span><span><span><math><mfenced><mrow><mtable><mtr><mtd></mtd><mtd><msub><mrow><mi>n</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>+</mo><mi>u</mi><mi>⋅</mi><mo>∇</mo><mi>n</mi><mo>=</mo><mo>∇</mo><mi>⋅</mi><mfenced><mrow><msup><mrow><mfenced><mrow><mo>∇</mo><mi>n</mi></mrow></mfenced></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow></msup><mo>∇</mo><mi>n</mi></mrow></mfenced><mo>−</mo><mi>χ</mi><mo>∇</mo><mi>⋅</mi><mrow><mo>(</mo><mfrac><mrow><mi>n</mi></mrow><mrow><mi>c</mi></mrow></mfrac><mo>∇</mo><mi>c</mi><mo>)</mo></mrow><mo>+</mo><mi>n</mi><mfenced><mrow><mi>r</mi><mo>−</mo><mi>μ</mi><msup><mrow><mi>n</mi></mrow><mrow><mi>δ</mi></mrow></msup></mrow></mfenced><mo>,</mo></mtd></mtr><mtr><mtd></mtd><mtd><msub><mrow><mi>c</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>+</mo><mi>u</mi><mi>⋅</mi><mo>∇</mo><mi>c</mi><mo>=</mo><mi>Δ</mi><mi>c</mi><mo>−</mo><mi>n</mi><mi>c</mi><mo>,</mo></mtd></mtr><mtr><mtd></mtd><mtd><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>=</mo><mi>Δ</mi><mi>u</mi><mo>+</mo><mo>∇</mo><mi>P</mi><mo>+</mo><mi>n</mi><mo>∇</mo><mi>Φ</mi></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>in a smooth bounded domain <span><math><mrow><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></math></span> with no-flux/no-flux/Dirichlet boundary conditions. It is shown that there exists a global weak solution when <span><math><mrow><mi>p</mi><mo>≥</mo><mn>2</mn></mrow></math></span> and <span><math><mrow><mi>δ</mi><mo>&gt;</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></math></span>, which removes the restriction <span><math><mrow><mi>p</mi><mo>&gt;</mo><mtext>min</mtext><mfenced><mrow><mfrac><mrow><mn>6</mn><mi>δ</mi><mo>+</mo><mn>1</mn></mrow><mrow><mn>2</mn><mfenced><mrow><mn>2</mn><mi>δ</mi><mo>−</mo><mn>1</mn></mrow></mfenced></mrow></mfrac><mo>,</mo><mfrac><mrow><mn>2</mn><mi>δ</mi><mfenced><mrow><mi>δ</mi><mo>+</mo><mn>2</mn></mrow></mfenced></mrow><mrow><mfenced><mrow><mn>2</mn><mi>δ</mi><mo>+</mo><mn>3</mn></mrow></mfenced><mfenced><mrow><mi>δ</mi><mo>−</mo><mn>1</mn></mrow></mfenced></mrow></mfrac></mrow></mfenced></mrow></math></span> and improves the result of the paper (Han and Liu, 2023).</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104339"},"PeriodicalIF":1.8,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143474962","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 class of time-dependent variational inequalities and their application in multi-layer contact systems","authors":"Zhizhuo Zhang ,&nbsp;Mikaël Barboteu ,&nbsp;Jinde Cao","doi":"10.1016/j.nonrwa.2025.104338","DOIUrl":"10.1016/j.nonrwa.2025.104338","url":null,"abstract":"<div><div>Based on the actual mechanical analysis of asphalt pavements, a class of multi-layer contact system problems with long memory terms and time-dependent interlayer contact conditions is proposed, and the corresponding time-dependent variational inequalities are further presented. Subsequently, based on general operator regularity assumptions, the existence, uniqueness, and regularity of the solutions to such variational inequalities over the unbounded time interval <span><math><msub><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msub></math></span>, as well as the stability of the solutions to the contact system over a bounded time interval <span><math><mrow><mi>I</mi><mo>=</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>]</mo></mrow></mrow></math></span>, are analyzed. Finally, through numerical experiments, the influence of long memory terms and time-dependent contact conditions on the multi-layer contact system is further discussed and interpreted. The theoretical and numerical results collectively verify the feasibility and value of studying nonlinear phenomena in contact problems by formulating variational inequalities.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104338"},"PeriodicalIF":1.8,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143454340","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 well-posedness of strong solutions to the 2D nonhomogeneous primitive equations with density-dependent viscosity","authors":"Quansen Jiu ,&nbsp;Lin Ma ,&nbsp;Fengchao Wang","doi":"10.1016/j.nonrwa.2025.104337","DOIUrl":"10.1016/j.nonrwa.2025.104337","url":null,"abstract":"<div><div>In this paper, we consider the initial–boundary value problem of the nonhomogeneous primitive equations with density-dependent viscosity. Local well-posedness of strong solutions is established for this system with a natural compatibility condition. The initial density does not need to be strictly positive and may contain vacuum. Meanwhile, we also give the corresponding blow-up criterion if the maximum existence interval with respect to the time is finite.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104337"},"PeriodicalIF":1.8,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143454339","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":"Sharp well-posedness and ill-posedness results for the inhomogeneous NLS equation","authors":"Luccas Campos ,&nbsp;Simão Correia ,&nbsp;Luiz Gustavo Farah","doi":"10.1016/j.nonrwa.2025.104336","DOIUrl":"10.1016/j.nonrwa.2025.104336","url":null,"abstract":"<div><div>We consider the initial value problem associated to the inhomogeneous nonlinear Schrödinger equation, <span><span><span><math><mrow><mi>i</mi><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>+</mo><mi>Δ</mi><mi>u</mi><mo>+</mo><mi>μ</mi><msup><mrow><mrow><mo>|</mo><mi>x</mi><mo>|</mo></mrow></mrow><mrow><mo>−</mo><mi>b</mi></mrow></msup><msup><mrow><mrow><mo>|</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mi>α</mi></mrow></msup><mi>u</mi><mo>=</mo><mn>0</mn><mo>,</mo><mspace></mspace><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><msup><mrow><mi>H</mi></mrow><mrow><mi>s</mi></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>)</mo></mrow><mspace></mspace><mtext>or</mtext><mspace></mspace><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><msup><mrow><mover><mrow><mi>H</mi></mrow><mrow><mo>̇</mo></mrow></mover></mrow><mrow><mi>s</mi></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>)</mo></mrow><mo>,</mo></mrow></math></span></span></span>with <span><math><mrow><mi>μ</mi><mo>=</mo><mo>±</mo><mn>1</mn></mrow></math></span>, <span><math><mrow><mi>b</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>, <span><math><mrow><mi>s</mi><mo>≥</mo><mn>0</mn></mrow></math></span> and <span><math><mrow><mn>0</mn><mo>&lt;</mo><mi>α</mi><mo>≤</mo><mfrac><mrow><mn>4</mn><mo>−</mo><mn>2</mn><mi>b</mi></mrow><mrow><mi>N</mi><mo>−</mo><mn>2</mn><mi>s</mi></mrow></mfrac></mrow></math></span> (<span><math><mrow><mn>0</mn><mo>&lt;</mo><mi>α</mi><mo>&lt;</mo><mi>∞</mi></mrow></math></span> if <span><math><mrow><mi>s</mi><mo>≥</mo><mi>N</mi><mo>/</mo><mn>2</mn></mrow></math></span>). By means of an adapted version of the fractional Leibniz rule, we prove new local well-posedness results in Sobolev spaces for a large range of parameters. We also prove an ill-posedness result for this equation, through a delicate analysis of the associated Duhamel operator.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104336"},"PeriodicalIF":1.8,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143445533","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":"D1,p(RN) versus Cb(RN,1+|x|N−pp−1α) local minimizers","authors":"Siegfried Carl ,&nbsp;Hossein Tehrani","doi":"10.1016/j.nonrwa.2025.104335","DOIUrl":"10.1016/j.nonrwa.2025.104335","url":null,"abstract":"<div><div>Let <span><math><mrow><mi>X</mi><mo>=</mo><msup><mrow><mi>D</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>p</mi></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span> be the Beppo-Levi space (homogeneous Sobolev space) with <span><math><mrow><mn>2</mn><mo>≤</mo><mi>p</mi><mo>&lt;</mo><mi>N</mi></mrow></math></span>, and for <span><math><mrow><mfrac><mrow><mi>p</mi><mo>−</mo><mn>1</mn></mrow><mrow><mi>p</mi></mrow></mfrac><mo>&lt;</mo><mi>α</mi><mo>≤</mo><mn>1</mn></mrow></math></span> let <span><math><mrow><msub><mrow><mi>V</mi></mrow><mrow><mi>α</mi></mrow></msub><mo>=</mo><mi>X</mi><mo>∩</mo><msub><mrow><mi>C</mi></mrow><mrow><mi>b</mi></mrow></msub><mrow><mo>(</mo><mrow><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>,</mo><mn>1</mn><mo>+</mo><msup><mrow><mrow><mo>|</mo><mi>x</mi><mo>|</mo></mrow></mrow><mrow><mfrac><mrow><mi>N</mi><mo>−</mo><mi>p</mi></mrow><mrow><mi>p</mi><mo>−</mo><mn>1</mn></mrow></mfrac><mi>α</mi></mrow></msup></mrow><mo>)</mo></mrow></mrow></math></span> be the subspace of bounded continuous functions with weight <span><math><mrow><mn>1</mn><mo>+</mo><msup><mrow><mrow><mo>|</mo><mi>x</mi><mo>|</mo></mrow></mrow><mrow><mfrac><mrow><mi>N</mi><mo>−</mo><mi>p</mi></mrow><mrow><mi>p</mi><mo>−</mo><mn>1</mn></mrow></mfrac><mi>α</mi></mrow></msup></mrow></math></span>. In this paper we prove a Brezis-Nirenberg type result for the energy functional <span><math><mrow><mi>Φ</mi><mo>:</mo><mi>X</mi><mo>→</mo><mi>R</mi></mrow></math></span> related to the quasilinear elliptic equation in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span> of the form <span><span><span><math><mrow><mi>u</mi><mo>∈</mo><mi>X</mi><mo>:</mo><mo>−</mo><msub><mrow><mi>Δ</mi></mrow><mrow><mi>p</mi></mrow></msub><mi>u</mi><mo>=</mo><mi>a</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>g</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mspace></mspace><mtext>in</mtext><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>,</mo></mrow></math></span></span></span>which states that a local minimizer of <span><math><mi>Φ</mi></math></span> in the <span><math><msub><mrow><mi>V</mi></mrow><mrow><mi>α</mi></mrow></msub></math></span>-topology must be a local minimizer in the ”bigger” <span><math><mi>X</mi></math></span>-topology.</div><div>Global <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup></math></span>-estimates for solutions of general quasilinear elliptic equations of divergence type in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span> on the one hand, and decay estimates for solutions of <span><math><mi>p</mi></math></span>-Laplace equations via nonlinear Wolff potentials as well as comparison theorems for <span><math><mi>p</mi></math></span>-Laplacian type operators on the other hand play an important role in the proofs.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104335"},"PeriodicalIF":1.8,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143436425","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":"Double phase problems with variable exponents depending on the solution and the gradient in the whole space RN","authors":"Ala Eddine Bahrouni ,&nbsp;Anouar Bahrouni ,&nbsp;Patrick Winkert","doi":"10.1016/j.nonrwa.2025.104334","DOIUrl":"10.1016/j.nonrwa.2025.104334","url":null,"abstract":"<div><div>In this paper, we establish continuous and compact embeddings for a new class of Musielak-Orlicz Sobolev spaces in unbounded domains driven by a double phase operator with variable exponents that depend on the unknown solution and its gradient. Using these embeddings and an abstract critical point theorem, we prove the existence and multiplicity of weak solutions for such problems associated with this new operator in the whole space <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>. This work can be seen as a continuation of the recent paper by Bahrouni–Bahrouni–Missaoui–Rădulescu (Bahrouni et al., 2024).</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104334"},"PeriodicalIF":1.8,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143420684","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 existence via starvation-driven ratio-dependent motility in chemotaxis consumption models","authors":"Changwook Yoon","doi":"10.1016/j.nonrwa.2025.104330","DOIUrl":"10.1016/j.nonrwa.2025.104330","url":null,"abstract":"<div><div>In this study, we introduce a chemotaxis consumption model incorporating a motility function designed to quantify the average resource availability per individual. This model is developed in the context of biological systems, where starvation due to increased population or limited resources encourages organisms to disperse more actively. Our research focuses on the global existence of classical solutions in bounded domains of any spatial dimension.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104330"},"PeriodicalIF":1.8,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143403280","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":"Interface disappearance in fast reaction limit","authors":"Yuki Tsukamoto","doi":"10.1016/j.nonrwa.2025.104333","DOIUrl":"10.1016/j.nonrwa.2025.104333","url":null,"abstract":"<div><div>We study the singular limit problem referred to as the fast reaction limit. This problem has been extensively studied when the same reaction term is used in a two-component system. However, the behavior of the solution under different reaction terms remains not yet well understood. In this paper, we will consider the problem where the reaction term is represented by a power term. When the reaction term is appropriate, we prove that the initial interface disappears immediately, and the function converges to a solution that satisfies the heat equation.</div></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"85 ","pages":"Article 104333"},"PeriodicalIF":1.8,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143394997","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}