Nonlinear Analysis-Real World Applications最新文献

{"title":"Global-in-time error estimates of non-relativistic limits for Euler–Maxwell system near non-constant equilibrium","authors":"Yachun Li ,&nbsp;Peng Lu ,&nbsp;Liang Zhao","doi":"10.1016/j.nonrwa.2024.104163","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104163","url":null,"abstract":"<div><p>It was proved that Euler–Maxwell systems converge globally-in-time to Euler–Poisson systems near non-constant equilibrium states when the speed of light <span><math><mrow><mi>c</mi><mo>→</mo><mi>∞</mi></mrow></math></span>. In this paper, we establish the global-in-time error estimates between smooth solutions of Euler–Maxwell systems and those of Euler–Poisson systems near non-constant equilibrium states. The main difficulty lies in the singularity of the error variable for the electric field <span><math><mi>E</mi></math></span>, so that more careful estimates for the time derivatives of error variables should be established. The proof takes good advantage of the anti-symmetric structure of the error system and an induction argument on the order of the derivatives.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141482153","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":"Parabolic double phase obstacle problems","authors":"Siegfried Carl ,&nbsp;Patrick Winkert","doi":"10.1016/j.nonrwa.2024.104169","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104169","url":null,"abstract":"<div><p>We prove existence results for the parabolic double phase obstacle problem: Find <span><math><mrow><mi>u</mi><mo>∈</mo><mi>K</mi><mo>⊂</mo><msub><mrow><mi>X</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></math></span> with <span><math><mrow><mi>u</mi><mrow><mo>(</mo><mi>⋅</mi><mo>,</mo><mn>0</mn><mo>)</mo></mrow><mo>=</mo><mn>0</mn></mrow></math></span> satisfying <span><span><span><math><mrow><mn>0</mn><mo>∈</mo><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>+</mo><mi>A</mi><mi>u</mi><mo>+</mo><mi>F</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mo>+</mo><mi>∂</mi><msub><mrow><mi>I</mi></mrow><mrow><mi>K</mi></mrow></msub><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mspace></mspace><mtext>in</mtext><msubsup><mrow><mi>X</mi></mrow><mrow><mn>0</mn></mrow><mrow><mo>∗</mo></mrow></msubsup><mo>,</mo></mrow></math></span></span></span>where <span><math><mrow><mi>A</mi><mo>:</mo><msub><mrow><mi>X</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>→</mo><msubsup><mrow><mi>X</mi></mrow><mrow><mn>0</mn></mrow><mrow><mo>∗</mo></mrow></msubsup></mrow></math></span> given by <span><span><span><math><mrow><mi>A</mi><mi>u</mi><mo>≔</mo><mo>−</mo><mo>div</mo><mfenced><mrow><msup><mrow><mo>|</mo><mo>∇</mo><mi>u</mi><mo>|</mo></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow></msup><mo>∇</mo><mi>u</mi><mo>+</mo><mi>μ</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><msup><mrow><mo>|</mo><mo>∇</mo><mi>u</mi><mo>|</mo></mrow><mrow><mi>q</mi><mo>−</mo><mn>2</mn></mrow></msup><mo>∇</mo><mi>u</mi></mrow></mfenced><mspace></mspace><mtext>for</mtext><mi>u</mi><mo>∈</mo><msub><mrow><mi>X</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo></mrow></math></span></span></span>is the double phase operator acting on <span><math><mrow><msub><mrow><mi>X</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>τ</mi><mo>;</mo><msubsup><mrow><mi>W</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>1</mn><mo>,</mo><mi>H</mi></mrow></msubsup><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow></math></span> with <span><math><mrow><msubsup><mrow><mi>W</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>1</mn><mo>,</mo><mi>H</mi></mrow></msubsup><mrow><mo>(</mo><mi>Ω</mi><mo>)</mo></mrow></mrow></math></span> denoting the associated Musielak–Orlicz Sobolev space with generalized homogeneous boundary values. The obstacle is represented by the closed convex set <span><math><mi>K</mi></math></span> with the obstacle function <span><math><mi>ψ</mi></math></span> through <span><span><span><math><mrow><mi>K</mi><mo>=</mo><mrow><mo>{</mo><mi>v</mi><mo>∈</mo><msub><mrow><mi>X</mi></mrow><mrow><mn>0</mn></mrow></msub><mspace></mspace><mo>:</mo><mspace></mspace><mi>v</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow><mo>≤</mo><mi>ψ</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow><mtext>for a.a.</mtext><mspace></mspace><mrow><mo>(</mo><mi>x</mi><mo>,<","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1468121824001093/pdfft?md5=8c45c9bac4bc0752dc7ba149da99cd83&pid=1-s2.0-S1468121824001093-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141480008","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":"Multiple standing waves of matrix nonlinear Schrödinger equations with mixed growth nonlinearities in RN","authors":"Ting Zhang,&nbsp;Guanwei Chen","doi":"10.1016/j.nonrwa.2024.104153","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104153","url":null,"abstract":"<div><p>In the whole space <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span>, we study the existence of two standing waves for a class of matrix nonlinear Schrödinger equations with potentials by using variational methods, where the nonlinearities are sublinear or asymptotically linear at infinity. The novelties are as follows. (1) The matrix nonlinear equations are defined in the whole space <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span>. (2) The nonlinearities are composed of two mixed nonlinear terms with different growth conditions. (3) The weight function may be sign-changing. (4) Our results can be applied to many examples.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141481793","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 hybrid Krasnosel’skiĭ-Schauder fixed point theorem for systems","authors":"Gennaro Infante ,&nbsp;Giovanni Mascali ,&nbsp;Jorge Rodríguez–López","doi":"10.1016/j.nonrwa.2024.104165","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104165","url":null,"abstract":"<div><p>We provide new results regarding the localization of the solutions of nonlinear operator systems. We make use of a combination of Krasnosel’skiĭ cone compression–expansion type methodologies and Schauder-type ones. In particular we establish a localization of the solution of the system within the product of a conical shell and of a closed convex set. By iterating this procedure we prove the existence of multiple solutions. We illustrate our theoretical results by applying them to the solvability of systems of Hammerstein integral equations. In the case of two specific boundary value problems and with given nonlinearities, we are also able to obtain a numerical solution, consistent with our theoretical results.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1468121824001056/pdfft?md5=984ec1968dd493852031ece7dfb44f60&pid=1-s2.0-S1468121824001056-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141481797","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":"Local stability and topological structure of completely integrable differential systems","authors":"Yantao Yang ,&nbsp;Xiang Zhang ,&nbsp;Zhiyu Wang","doi":"10.1016/j.nonrwa.2024.104172","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104172","url":null,"abstract":"<div><p>Completely integrable systems are dynamically simple in common sense, but they may have complicated dynamics around the points where their first integrals are not functionally independent. Tudoran in 2017 provided a criterion for characterizing stability of nondegenerated regular singularities of completely integrable systems. Here we present a new criterion which is more useful than that by Tudoran, in the sense that the cases that his criterion works on are also applicable to ours, whereas there are cases that our criterion works on but his does not.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141481792","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":"Boundedness of weak solutions to a 3D chemotaxis-Stokes system with slow p−Laplacian diffusion and rotation","authors":"Haolan He,&nbsp;Zhongping Li","doi":"10.1016/j.nonrwa.2024.104164","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104164","url":null,"abstract":"<div><p>In this paper, we consider the following chemotaxis-Stokes system with general sensitivity and rotation <span><span><span><math><mfenced><mrow><mtable><mtr><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><mrow><mo>(</mo><msup><mrow><mrow><mo>|</mo><mo>∇</mo><mi>n</mi><mo>|</mo></mrow></mrow><mrow><mi>p</mi><mo>−</mo><mn>2</mn></mrow></msup><mo>∇</mo><mi>n</mi><mo>)</mo></mrow><mo>−</mo><mo>∇</mo><mi>⋅</mi><mrow><mo>(</mo><mi>n</mi><mi>S</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>n</mi><mo>,</mo><mi>c</mi><mo>)</mo></mrow><mo>∇</mo><mi>c</mi><mo>)</mo></mrow><mo>,</mo><mspace></mspace></mtd><mtd><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo><mi>t</mi><mo>&gt;</mo><mn>0</mn><mo>,</mo></mtd></mtr><mtr><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><mspace></mspace></mtd><mtd><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo><mi>t</mi><mo>&gt;</mo><mn>0</mn><mo>,</mo></mtd></mtr><mtr><mtd><msub><mrow><mi>u</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>+</mo><mo>∇</mo><mi>P</mi><mo>=</mo><mi>Δ</mi><mi>u</mi><mo>+</mo><mi>n</mi><mo>∇</mo><mi>ϕ</mi><mo>,</mo><mspace></mspace></mtd><mtd><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo><mi>t</mi><mo>&gt;</mo><mn>0</mn><mo>,</mo></mtd></mtr><mtr><mtd><mo>∇</mo><mi>⋅</mi><mi>u</mi><mo>=</mo><mn>0</mn><mo>,</mo><mspace></mspace></mtd><mtd><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo><mi>t</mi><mo>&gt;</mo><mn>0</mn></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 zero-flux boundary and no-slip boundary condition. We prove the boundedness of the weak solutions to the initial–boundary value problem of the 3D chemotaxis-Stokes system with <span><math><mrow><mi>p</mi><mo>−</mo></mrow></math></span>Laplacian diffusion if <span><math><mrow><mfrac><mrow><mn>4</mn></mrow><mrow><mn>3</mn></mrow></mfrac><mi>p</mi><mo>+</mo><mi>α</mi><mo>&gt;</mo><mfrac><mrow><mn>7</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>−</mo><mfrac><mrow><msqrt><mrow><mn>6</mn></mrow></msqrt></mrow><mrow><mn>3</mn></mrow></mfrac></mrow></math></span> and <span><math><mrow><mi>p</mi><mo>&gt;</mo><mn>2</mn></mrow></math></span>, which improves the results of papers [Chen et al., Nonlinear Anal. Real World Appl., 76 (2024) 103996; Zhuang et al., Nonlinear Anal. Real World Appl., 56 (2020) 103163 and Tao et al., J. Differ. Equ., 268(11) (2020) 6879–6919] and extends the result of the paper [Jin, J. Differ. Equ. 287 (2021) 148–184] to the chemotaxis system with general sensitivity and rotation.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141429260","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":"Erratum to “Chemotaxis systems with singular sensitivity and logistic source: Boundedness, persistence, absorbing set, and entire solutions” [Nonlinear Anal. Real World Appl. 69 (2023) 27]","authors":"Halil Ibrahim Kurt,&nbsp;Wenxian Shen","doi":"10.1016/j.nonrwa.2024.104141","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104141","url":null,"abstract":"<div><p>This note is to make some corrections on the conditions for the initial function <span><math><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> and the parameters in the system (1.1) in our paper Halil Ibrahim Kurt and Wenxian Shen (2023)</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1468121824000816/pdfft?md5=87abb43f898ed81e07f38244896cbe80&pid=1-s2.0-S1468121824000816-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141429261","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":"Local well-posedness of solutions to 2D mixed Prandtl equations in Sobolev space without monotonicity and lower bound","authors":"Yuming Qin ,&nbsp;Xiaolei Dong","doi":"10.1016/j.nonrwa.2024.104140","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104140","url":null,"abstract":"<div><p>In this paper, we investigate two-dimensional Prandtl–Shercliff regime equations on the half plane and prove the local existence and uniqueness of solutions for any initial datum by using the classical energy methods in Sobolev space. Compared to the existence and uniqueness of solutions to the classical Prandtl equations where the monotonicity condition of the tangential velocity plays a key role, this monotonicity condition is not needed for 2D mixed Prandtl equations. Besides, compared with the existence and uniqueness of solutions to the 2D MHD boundary layer where the initial tangential magnetic field has a lower bound plays an important role, this lower bound condition is also not needed for 2D mixed Prandtl equations. In other words, we need neither the monotonicity condition of the tangential velocity nor the initial tangential magnetic field has a lower bound and for any initial datum in this paper. As far as we have learned, this is the first result of <span><math><mrow><mn>2</mn><mi>D</mi></mrow></math></span> mixed Prandtl–Shercliff regime equations in Sobolev space.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141322404","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":"General decay results for a viscoelastic wave equation with the logarithmic nonlinear source and dynamic Wentzell boundary condition","authors":"Dandan Guo ,&nbsp;Zhifei Zhang","doi":"10.1016/j.nonrwa.2024.104149","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104149","url":null,"abstract":"<div><p>In this work we investigate a viscoelastic wave equation involving a logarithmic nonlinear source and dynamic Wentzell boundary condition. Making some assumptions on the memory kernel function and using convex function theory and Lyapunov method, we establish the general decay estimate of the solutions. Finally we give two examples to illustrate our results.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141314166","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":"Principal eigenvalues for Fully Non Linear singular or degenerate operators in punctured balls","authors":"Françoise Demengel","doi":"10.1016/j.nonrwa.2024.104142","DOIUrl":"https://doi.org/10.1016/j.nonrwa.2024.104142","url":null,"abstract":"<div><p>This paper is devoted to the proof of the existence of the principal eigenvalue and related eigenfunctions for fully nonlinear degenerate or singular uniformly elliptic equations posed in a punctured ball, in presence of a singular potential. More precisely, we analyze existence, uniqueness and regularity of solutions <span><math><mrow><mo>(</mo><msub><mrow><mover><mrow><mi>λ</mi></mrow><mrow><mo>̄</mo></mrow></mover></mrow><mrow><mi>γ</mi></mrow></msub><mo>,</mo><msub><mrow><mi>u</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo>)</mo></mrow></math></span> of the equation <span><math><mrow><msup><mrow><mrow><mo>|</mo><mo>∇</mo><mi>u</mi><mo>|</mo></mrow></mrow><mrow><mi>α</mi></mrow></msup><mi>F</mi><mrow><mo>(</mo><msup><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msup><msub><mrow><mi>u</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo>)</mo></mrow><mo>+</mo><msub><mrow><mover><mrow><mi>λ</mi></mrow><mrow><mo>̄</mo></mrow></mover></mrow><mrow><mi>γ</mi></mrow></msub><mfrac><mrow><msubsup><mrow><mi>u</mi></mrow><mrow><mi>γ</mi></mrow><mrow><mn>1</mn><mo>+</mo><mi>α</mi></mrow></msubsup></mrow><mrow><msup><mrow><mi>r</mi></mrow><mrow><mi>γ</mi></mrow></msup></mrow></mfrac><mo>=</mo><mn>0</mn><mspace></mspace><mtext>in</mtext><mspace></mspace><mi>B</mi><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow><mo>∖</mo><mrow><mo>{</mo><mn>0</mn><mo>}</mo></mrow><mo>,</mo><mspace></mspace><msub><mrow><mi>u</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo>=</mo><mn>0</mn><mspace></mspace><mtext>on</mtext><mspace></mspace><mi>∂</mi><mi>B</mi><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span> where <span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo>&gt;</mo><mn>0</mn></mrow></math></span> in <span><math><mrow><mi>B</mi><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>, <span><math><mrow><mi>α</mi><mo>&gt;</mo><mo>−</mo><mn>1</mn></mrow></math></span> and <span><math><mrow><mi>γ</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span>. We prove existence of radial solutions which are continuous on <span><math><mover><mrow><mi>B</mi><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow><mo>¯</mo></mover></math></span> in the case <span><math><mrow><mi>γ</mi><mo>&lt;</mo><mn>2</mn><mo>+</mo><mi>α</mi></mrow></math></span>, and a non existence result for <span><math><mrow><mi>γ</mi><mo>&gt;</mo><mn>2</mn><mo>+</mo><mi>α</mi></mrow></math></span>. We also give the explicit value of <span><math><msub><mrow><mover><mrow><mi>λ</mi></mrow><mrow><mo>̄</mo></mrow></mover></mrow><mrow><mn>2</mn><mo>+</mo><mi>α</mi></mrow></msub></math></span> in the case of the Pucci’s operators, which generalizes the Hardy–Sobolev constant for the Laplacian, and the previous results of Birindelli et al. <span>[1]</span>.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":null,"pages":null},"PeriodicalIF":2.0,"publicationDate":"2024-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141308390","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}