Advances in Nonlinear Analysis最新文献

{"title":"Infinitely many solutions for Hamiltonian system with critical growth","authors":"Yuxia Guo, Yichen Hu","doi":"10.1515/anona-2023-0134","DOIUrl":"https://doi.org/10.1515/anona-2023-0134","url":null,"abstract":"\u0000 <jats:p>In this article, we consider the following elliptic system of Hamiltonian-type on a bounded domain:<jats:disp-formula id=\"j_anona-2023-0134_eq_001\">\u0000 <jats:alternatives>\u0000 <jats:graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_anona-2023-0134_eq_001.png\" />\u0000 <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" display=\"block\">\u0000 <m:mfenced open=\"{\" close=\"\">\u0000 <m:mrow>\u0000 <m:mtable displaystyle=\"true\">\u0000 <m:mtr>\u0000 <m:mtd columnalign=\"left\">\u0000 <m:mo>−</m:mo>\u0000 <m:mi mathvariant=\"normal\">Δ</m:mi>\u0000 <m:mi>u</m:mi>\u0000 <m:mo>=</m:mo>\u0000 <m:msub>\u0000 <m:mrow>\u0000 <m:mi>K</m:mi>\u0000 </m:mrow>\u0000 <m:mrow>\u0000 <m:mn>1</m:mn>\u0000 </m:mrow>\u0000 </m:msub>\u0000 <m:mrow>\u0000 <m:mo>(</m:mo>\u0000 <m:mrow>\u0000 <m:mo>∣</m:mo>\u0000 <m:mi>y</m:mi>\u0000 <m:mo>∣</m:mo>\u0000 </m:mrow>\u0000 <m:mo>)</m:mo>\u0000 </m:mrow>\u0000 <m:msup>\u0000 <m:mrow>\u0000 <m:mo>∣</m:mo>\u0000 <m:mi>v</m:mi>\u0000 <m:mo>∣</m:mo>\u0000 </m:mrow>\u0000 <m:mrow>\u0000 <m:mi>p</m:mi>\u0000 <m:mo>−</m:mo>\u0000 <m:mn>1</m:mn>\u0000 </m:mrow>\u0000 </m:msup>\u0000 <m:mi>v</m:mi>\u0000 <m:mo>,</m:mo>\u0000 <m:mspace width=\"1.0em\" />\u0000 </m:mtd>\u0000 <m:mtd columnalign=\"left\">\u0000 <m:mspace width=\"0.1em\" />\u0000 ","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140516657","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multiple positive solutions for a class of concave-convex Schrödinger-Poisson-Slater equations with critical exponent","authors":"Tian-Tian Zheng, Chun-Yu Lei, Jia-Feng Liao","doi":"10.1515/anona-2023-0129","DOIUrl":"https://doi.org/10.1515/anona-2023-0129","url":null,"abstract":"\u0000 <jats:p>In this article, we consider the multiplicity of positive solutions for a static Schrödinger-Poisson-Slater equation of the type <jats:disp-formula id=\"j_anona-2023-0129_eq_001\">\u0000 <jats:alternatives>\u0000 <jats:graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_anona-2023-0129_eq_001.png\" />\u0000 <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" display=\"block\">\u0000 <m:mo>−</m:mo>\u0000 <m:mi mathvariant=\"normal\">Δ</m:mi>\u0000 <m:mi>u</m:mi>\u0000 <m:mo>+</m:mo>\u0000 <m:mfenced open=\"(\" close=\")\">\u0000 <m:mrow>\u0000 <m:msup>\u0000 <m:mrow>\u0000 <m:mi>u</m:mi>\u0000 </m:mrow>\u0000 <m:mrow>\u0000 <m:mn>2</m:mn>\u0000 </m:mrow>\u0000 </m:msup>\u0000 <m:mo>∗</m:mo>\u0000 <m:mfrac>\u0000 <m:mrow>\u0000 <m:mn>1</m:mn>\u0000 </m:mrow>\u0000 <m:mrow>\u0000 <m:mo>∣</m:mo>\u0000 <m:mn>4</m:mn>\u0000 <m:mi>π</m:mi>\u0000 <m:mi>x</m:mi>\u0000 <m:mo>∣</m:mo>\u0000 </m:mrow>\u0000 </m:mfrac>\u0000 </m:mrow>\u0000 </m:mfenced>\u0000 <m:mi>u</m:mi>\u0000 <m:mo>=</m:mo>\u0000 <m:mi>μ</m:mi>\u0000 <m:mi>f</m:mi>\u0000 <m:mrow>\u0000 <m:mo>(</m:mo>\u0000 <m:mrow>\u0000 <m:mi>x</m:mi>\u0000 </m:mrow>\u0000 <m:mo>)</m:mo>\u0000 </m:mrow>\u0000 <m:msup>\u0000 <m:mrow>\u0000 <m:mo>∣</m:mo>\u0000 <m:mi>u</m:mi>\u0000 <m:mo>∣</m:mo>\u0000 </m:mrow>\u0000 <m:mrow>\u0000 <m:mi>p</m:mi>\u0000 <m:mo>−</m:mo>\u0000 <m:mn>2</m:mn>\u0000 </m:mrow>\u0000 </m:msup>\u0000 <m:mi>u</m:mi>\u0000 <m:mo>+</m:mo>\u0000 <m:mi>g</m:mi>\u0000 <m:mrow>\u0000 ","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140522278","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Existence, uniqueness, localization and minimization property of positive solutions for non-local problems involving discontinuous Kirchhoff functions","authors":"B. Ricceri","doi":"10.1515/anona-2023-0104","DOIUrl":"https://doi.org/10.1515/anona-2023-0104","url":null,"abstract":"\u0000 <jats:p>Let <jats:inline-formula>\u0000 <jats:alternatives>\u0000 <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_anona-2023-0104_eq_001.png\" />\u0000 <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\u0000 <m:mi mathvariant=\"normal\">Ω</m:mi>\u0000 <m:mo>⊂</m:mo>\u0000 <m:msup>\u0000 <m:mrow>\u0000 <m:mi mathvariant=\"bold\">R</m:mi>\u0000 </m:mrow>\u0000 <m:mrow>\u0000 <m:mi>n</m:mi>\u0000 </m:mrow>\u0000 </m:msup>\u0000 </m:math>\u0000 <jats:tex-math>Omega subset {{bf{R}}}^{n}</jats:tex-math>\u0000 </jats:alternatives>\u0000 </jats:inline-formula> be a smooth bounded domain. In this article, we prove a result of which the following is a by-product: Let <jats:inline-formula>\u0000 <jats:alternatives>\u0000 <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_anona-2023-0104_eq_002.png\" />\u0000 <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\u0000 <m:mi>q</m:mi>\u0000 <m:mo>∈</m:mo>\u0000 <m:mrow>\u0000 <m:mo stretchy=\"false\">]</m:mo>\u0000 <m:mrow>\u0000 <m:mn>0</m:mn>\u0000 <m:mo>,</m:mo>\u0000 <m:mn>1</m:mn>\u0000 </m:mrow>\u0000 <m:mo stretchy=\"false\">[</m:mo>\u0000 </m:mrow>\u0000 </m:math>\u0000 <jats:tex-math>qin ]0,1{[}</jats:tex-math>\u0000 </jats:alternatives>\u0000 </jats:inline-formula>, <jats:inline-formula>\u0000 <jats:alternatives>\u0000 <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_anona-2023-0104_eq_003.png\" />\u0000 <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\u0000 <m:mi>α</m:mi>\u0000 <m:mo>∈</m:mo>\u0000 <m:msup>\u0000 <m:mrow>\u0000 <m:mi>L</m:mi>\u0000 </m:mrow>\u0000 <m:mrow>\u0000 <m:mi>∞</m:mi>\u0000 </m:mrow>\u0000 </m:msup>\u0000 <m:mrow>\u0000 <m:mo>(</m:mo>\u0000 <m:mrow>\u0000 <m:mi mathvariant=\"normal\">Ω</m:mi>\u0000 </m:mrow>\u0000 <m:mo>)</m","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140519417","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Gradient estimates for a class of higher-order elliptic equations of p-growth over a nonsmooth domain","authors":"H. Tian, Shenzhou Zheng","doi":"10.1515/anona-2023-0132","DOIUrl":"https://doi.org/10.1515/anona-2023-0132","url":null,"abstract":"\u0000 <jats:p>This article is devoted to a global Calderón-Zygmund estimate in the framework of Lorentz spaces for the <jats:inline-formula>\u0000 <jats:alternatives>\u0000 <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_anona-2023-0132_eq_001.png\" />\u0000 <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\u0000 <m:mi>m</m:mi>\u0000 </m:math>\u0000 <jats:tex-math>m</jats:tex-math>\u0000 </jats:alternatives>\u0000 </jats:inline-formula>-order gradients of weak solution to a higher-order elliptic equation with <jats:inline-formula>\u0000 <jats:alternatives>\u0000 <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_anona-2023-0132_eq_002.png\" />\u0000 <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\u0000 <m:mi>p</m:mi>\u0000 </m:math>\u0000 <jats:tex-math>p</jats:tex-math>\u0000 </jats:alternatives>\u0000 </jats:inline-formula>-growth. We prove the main result based on a proper power decay estimation of the upper-level set by the principle of layer cake representation for the <jats:inline-formula>\u0000 <jats:alternatives>\u0000 <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_anona-2023-0132_eq_003.png\" />\u0000 <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\u0000 <m:msup>\u0000 <m:mrow>\u0000 <m:mi>L</m:mi>\u0000 </m:mrow>\u0000 <m:mrow>\u0000 <m:mi>γ</m:mi>\u0000 <m:mo>,</m:mo>\u0000 <m:mi>q</m:mi>\u0000 </m:mrow>\u0000 </m:msup>\u0000 </m:math>\u0000 <jats:tex-math>{L}^{gamma ,q}</jats:tex-math>\u0000 </jats:alternatives>\u0000 </jats:inline-formula>-estimate of <jats:inline-formula>\u0000 <jats:alternatives>\u0000 <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_anona-2023-0132_eq_004.png\" />\u0000 <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\u0000 <m:msup>\u0000 <m:mrow>\u0000 <m:mi>D</m:mi>\u0000 </m:mrow>\u0000 <m:mrow>\u0000 <m:mi>m</m:mi>\u0000 </m:mrow>\u0000 </m:msup>\u0000 <m:mi>u</m:mi>\u0000 </m:math>\u0000 <jats:tex-math>{D}^{m}u</jats:tex-mat","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140522805","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global existence and finite-time blowup for a mixed pseudo-parabolic r(x)-Laplacian equation","authors":"Jiazhuo Cheng, Qiru Wang","doi":"10.1515/anona-2023-0133","DOIUrl":"https://doi.org/10.1515/anona-2023-0133","url":null,"abstract":"\u0000 This article is devoted to the study of the initial boundary value problem for a mixed pseudo-parabolic \u0000 \u0000 \u0000 \u0000 r\u0000 \u0000 (\u0000 \u0000 x\u0000 \u0000 )\u0000 \u0000 \u0000 rleft(x)\u0000 \u0000 -Laplacian-type equation. First, by employing the imbedding theorems, the theory of potential wells, and the Galerkin method, we establish the existence and uniqueness of global solutions with subcritical initial energy, critical initial energy, and supercritical initial energy, respectively. Then, we obtain the decay estimate of global solutions with sub-sharp-critical initial energy, sharp-critical initial energy, and supercritical initial energy, respectively. For supercritical initial energy, we also need to analyze the properties of \u0000 \u0000 \u0000 \u0000 ω\u0000 \u0000 omega \u0000 \u0000 -limits of solutions. Finally, we discuss the finite-time blowup of solutions with sub-sharp-critical initial energy and sharp-critical initial energy, respectively.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140525963","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Beyond the classical strong maximum principle: Sign-changing forcing term and flat solutions","authors":"Jesús Ildefonso Díaz, J. Hernandez","doi":"10.1515/anona-2023-0128","DOIUrl":"https://doi.org/10.1515/anona-2023-0128","url":null,"abstract":"\u0000 We show that the classical strong maximum principle, concerning positive supersolutions of linear elliptic equations vanishing on the boundary of the domain can be extended, under suitable conditions, to the case in which the forcing term is sign-changing. In addition, for the case of solutions, the normal derivative on the boundary may also vanish on the boundary (definition of flat solution). This leads to examples in which the unique continuation property fails. As a first application, we show the existence of positive solutions for a sublinear semilinear elliptic problem of indefinite sign. A second application, concerning the positivity of solutions of the linear heat equation, for some large values of time, with forcing and/or initial datum changing sign, is also given.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140519792","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Variational–hemivariational system for contaminant convection–reaction–diffusion model of recovered fracturing fluid","authors":"Jinxia Cen, Stanisław Migórski, Jen-Chih Yao, Shengda Zeng","doi":"10.1515/anona-2023-0141","DOIUrl":"https://doi.org/10.1515/anona-2023-0141","url":null,"abstract":"\u0000 This work is devoted to study the convection–reaction–diffusion behavior of contaminant in the recovered fracturing fluid which flows in the wellbore from shale gas reservoir. First, we apply various constitutive laws for generalized non-Newtonian fluids, diffusion principles, and friction relations to formulate the recovered fracturing fluid model. The latter is a partial differential system composed of a nonlinear and nonsmooth stationary incompressible Navier-Stokes equation with a multivalued friction boundary condition, and a nonlinear convection–reaction–diffusion equation with mixed Neumann boundary conditions. Then, we provide the weak formulation of the fluid model which is a hemivariational inequality driven by a nonlinear variational equation. We establish existence of solutions to the recovered fracturing fluid model via a surjectivity theorem for multivalued operators combined with an alternative iterative method and elements of nonsmooth analysis.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140518775","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Orbital stability of the trains of peaked solitary waves for the modified Camassa-Holm-Novikov equation","authors":"Ting Luo","doi":"10.1515/anona-2023-0124","DOIUrl":"https://doi.org/10.1515/anona-2023-0124","url":null,"abstract":"\u0000 Consideration herein is the stability issue of peaked solitary wave solution for the modified Camassa-Holm-Novikov equation, which is derived from the shallow water theory. This wave configuration accommodates the ordered trains of the modified Camassa-Holm-Novikov-peaked solitary solution. With the application of conservation laws and the monotonicity property of the localized energy functionals, we prove the orbital stability of this wave profile in the \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 H\u0000 \u0000 \u0000 1\u0000 \u0000 \u0000 \u0000 (\u0000 \u0000 R\u0000 \u0000 )\u0000 \u0000 \u0000 {H}^{1}left({mathbb{R}})\u0000 \u0000 energy space according to the modulation argument.","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140521511","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global boundedness in a two-dimensional chemotaxis system with nonlinear diffusion and singular sensitivity","authors":"Guoqiang Ren, Xing Zhou","doi":"10.1515/anona-2023-0125","DOIUrl":"https://doi.org/10.1515/anona-2023-0125","url":null,"abstract":"\u0000 <jats:p>In this study, we investigate the two-dimensional chemotaxis system with nonlinear diffusion and singular sensitivity: <jats:disp-formula id=\"j_anona-2023-0125_eq_001\">\u0000 <jats:alternatives>\u0000 <jats:graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_anona-2023-0125_eq_001.png\" />\u0000 <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" display=\"block\">\u0000 <m:mfenced open=\"{\" close=\"\">\u0000 <m:mrow>\u0000 <m:mtable displaystyle=\"true\">\u0000 <m:mtr>\u0000 <m:mtd columnalign=\"left\">\u0000 <m:msub>\u0000 <m:mrow>\u0000 <m:mi>u</m:mi>\u0000 </m:mrow>\u0000 <m:mrow>\u0000 <m:mi>t</m:mi>\u0000 </m:mrow>\u0000 </m:msub>\u0000 <m:mo>=</m:mo>\u0000 <m:mrow>\u0000 <m:mo>∇</m:mo>\u0000 </m:mrow>\u0000 <m:mo>⋅</m:mo>\u0000 <m:mrow>\u0000 <m:mo>(</m:mo>\u0000 <m:mrow>\u0000 <m:msup>\u0000 <m:mrow>\u0000 <m:mi>u</m:mi>\u0000 </m:mrow>\u0000 <m:mrow>\u0000 <m:mi>θ</m:mi>\u0000 <m:mo>−</m:mo>\u0000 <m:mn>1</m:mn>\u0000 </m:mrow>\u0000 </m:msup>\u0000 <m:mrow>\u0000 <m:mo>∇</m:mo>\u0000 </m:mrow>\u0000 <m:mi>u</m:mi>\u0000 </m:mrow>\u0000 <m:mo>)</m:mo>\u0000 </m:mrow>\u0000 <m:mo>−</m:mo>\u0000 <m:mi>χ</m:mi>\u0000 <m:mrow>\u0000 <m:mo>∇</m:mo>\u0000 </m:mrow>\u0000 <m:mo>⋅</m:mo>\u0000 ","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140526435","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Vanishing and blow-up solutions to a class of nonlinear complex differential equations near the singular point","authors":"J. Diblík, M. Ruzicková","doi":"10.1515/anona-2023-0120","DOIUrl":"https://doi.org/10.1515/anona-2023-0120","url":null,"abstract":"\u0000 <jats:p>A singular nonlinear differential equation <jats:disp-formula id=\"j_anona-2023-0120_eq_001\">\u0000 <jats:alternatives>\u0000 <jats:graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_anona-2023-0120_eq_001.png\" />\u0000 <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\" display=\"block\">\u0000 <m:msup>\u0000 <m:mrow>\u0000 <m:mi>z</m:mi>\u0000 </m:mrow>\u0000 <m:mrow>\u0000 <m:mi>σ</m:mi>\u0000 </m:mrow>\u0000 </m:msup>\u0000 <m:mfrac>\u0000 <m:mrow>\u0000 <m:mi mathvariant=\"normal\">d</m:mi>\u0000 <m:mi>w</m:mi>\u0000 </m:mrow>\u0000 <m:mrow>\u0000 <m:mi mathvariant=\"normal\">d</m:mi>\u0000 <m:mi>z</m:mi>\u0000 </m:mrow>\u0000 </m:mfrac>\u0000 <m:mo>=</m:mo>\u0000 <m:mi>a</m:mi>\u0000 <m:mi>w</m:mi>\u0000 <m:mo>+</m:mo>\u0000 <m:mi>z</m:mi>\u0000 <m:mi>w</m:mi>\u0000 <m:mi>f</m:mi>\u0000 <m:mrow>\u0000 <m:mo>(</m:mo>\u0000 <m:mrow>\u0000 <m:mi>z</m:mi>\u0000 <m:mo>,</m:mo>\u0000 <m:mi>w</m:mi>\u0000 </m:mrow>\u0000 <m:mo>)</m:mo>\u0000 </m:mrow>\u0000 <m:mo>,</m:mo>\u0000 </m:math>\u0000 <jats:tex-math>{z}^{sigma }frac{{rm{d}}w}{{rm{d}}z}=aw+zwfleft(z,w),</jats:tex-math>\u0000 </jats:alternatives>\u0000 </jats:disp-formula> where <jats:inline-formula>\u0000 <jats:alternatives>\u0000 <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_anona-2023-0120_eq_002.png\" />\u0000 <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\u0000 <m:mi>σ</m:mi>\u0000 <m:mo>></m:mo>\u0000 <m:mn>1</m:mn>\u0000 </m:math>\u0000 <jats:tex-math>sigma gt 1</jats:tex-math>\u0000 </jats:alternatives>\u0000 </jats:inline-formula>, is considered in a neighbourhood of the point <jats:inline-formula>\u0000 <jats:alternatives>\u0000 <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_anona-2023-0120_eq_003.png\" />\u0000 <m","PeriodicalId":51301,"journal":{"name":"Advances in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":4.2,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140525677","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}