{"title":"Pohožaev-type ground state solutions for Choquard equation with singular potential and critical exponent","authors":"Senli Liu, Haibo Chen","doi":"10.12775/tmna.2021.052","DOIUrl":"https://doi.org/10.12775/tmna.2021.052","url":null,"abstract":"<jats:p />","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45855954","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Topological entropy of diagonal maps on inverse limit spaces","authors":"Ana Anušić, Christopher Mouron","doi":"10.12775/tmna.2021.043","DOIUrl":"https://doi.org/10.12775/tmna.2021.043","url":null,"abstract":"<jats:p />","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44387057","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"New fixed point theorems for sum operators in set $P_{h,e}$ and their applications to nonlinear fractional differential problems","authors":"Lingling Zhang, Huimin Tian","doi":"10.12775/tmna.2021.008","DOIUrl":"https://doi.org/10.12775/tmna.2021.008","url":null,"abstract":"<jats:p />","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47182883","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Equilibrium under uncertainty with fuzzy payoff","authors":"Taras Radul","doi":"10.12775/tmna.2021.049","DOIUrl":"https://doi.org/10.12775/tmna.2021.049","url":null,"abstract":"<jats:p />","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47386696","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Marcos Coutinho Mota, Alex Carlucci Rezende, Dana Schlomiuk, Nicolae Vulpe
{"title":"Geometric analysis of quadratic differential systems with invariant ellipses","authors":"Marcos Coutinho Mota, Alex Carlucci Rezende, Dana Schlomiuk, Nicolae Vulpe","doi":"10.12775/tmna.2021.063","DOIUrl":"https://doi.org/10.12775/tmna.2021.063","url":null,"abstract":"<jats:p />","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46337560","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Remarks on criticality and crisis in pure exchange economies","authors":"Jacobo Pejsachowicz","doi":"10.12775/tmna.2021.065","DOIUrl":"https://doi.org/10.12775/tmna.2021.065","url":null,"abstract":"<jats:p />","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":"34 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41300942","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We prove the existence of critical points of vortex type Hamiltonians [ H(p_1,ldots, p_N) = sum_{{i,j=1}atop{ine j}} ^N Gamma_iGamma_jG(p_i,p_j)+Psi(p_1,dots,p_N) ] on a closed Riemannian surface $(Sigma,g)$ which is not homeomorphic to the sphere or the projective plane. Here $G$ denotes the Green function of the Laplace-Beltrami operator in $Sigma$, $Psicolon Sigma^Ntomathbb{R}$ may be any function of class ${mathcal C}^1$, and $Gamma_1,dots,Gamma_Ninmathbb{R}setminus{0}$ are the vorticities. The Kirchhoff-Routh Hamiltonian from fluid dynamics corresponds to $Psi(p) = -sumlimits_{i=1}^N Gamma_i^2h(p_i,p_i)$ where $hcolon SigmatimesSigmatomathbb{R}$ is the regular part of the Laplace-Beltrami operator. We obtain critical points $p=(p_1,dots,p_N)$ for arbitrary $N$ and vorticities $(Gamma_1,dots,Gamma_N)$ in $mathbb{R}^Nsetminus V$ where $V$ is an explicitly given algebraic variety of codimension 1.
{"title":"Equilibria of vortex type Hamiltonians on closed surfaces","authors":"M. Ahmedou, T. Bartsch, Tim Fiernkranz","doi":"10.12775/tmna.2023.003","DOIUrl":"https://doi.org/10.12775/tmna.2023.003","url":null,"abstract":"We prove the existence of critical points of vortex type Hamiltonians\u0000 [\u0000 H(p_1,ldots, p_N)\u0000 = sum_{{i,j=1}atop{ine j}}\u0000^N Gamma_iGamma_jG(p_i,p_j)+Psi(p_1,dots,p_N)\u0000 ]\u0000on a closed Riemannian surface $(Sigma,g)$ which is not homeomorphic to the sphere\u0000or the projective plane. Here $G$ denotes the Green function of the Laplace-Beltrami\u0000 operator in $Sigma$, $Psicolon Sigma^Ntomathbb{R}$ may be any function of class ${mathcal C}^1$,\u0000and $Gamma_1,dots,Gamma_Ninmathbb{R}setminus{0}$ are the vorticities.\u0000 The Kirchhoff-Routh Hamiltonian from fluid dynamics corresponds to\u0000 $Psi(p) = -sumlimits_{i=1}^N Gamma_i^2h(p_i,p_i)$ where\u0000$hcolon SigmatimesSigmatomathbb{R}$ is the regular part of the Laplace-Beltrami operator.\u0000We obtain critical points $p=(p_1,dots,p_N)$ for arbitrary $N$ and vorticities\u0000$(Gamma_1,dots,Gamma_N)$ in $mathbb{R}^Nsetminus V$ where $V$ is an explicitly given algebraic variety of codimension 1.","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44592004","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Liouville-type theorems for generalized Hénon-Lane-Emden Schrödinger systems in $R^2$ and $R^3$","authors":"Xiyou Cheng, Kui Li, Zhitao Zhang","doi":"10.12775/tmna.2021.028","DOIUrl":"https://doi.org/10.12775/tmna.2021.028","url":null,"abstract":"<jats:p />","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48444103","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the Choquard equations under the effect of a general nonlinear term","authors":"Jiu Liu, Jia-Feng Liao, Hui-Lan Pan, Chun-Lei Tang","doi":"10.12775/tmna.2021.037","DOIUrl":"https://doi.org/10.12775/tmna.2021.037","url":null,"abstract":"<jats:p />","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48657825","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A heterogeneous diffusive logistic model with constant yield harvesting in $mathbb{R^N}$ under strong growth rate","authors":"Hossein Tehrani","doi":"10.12775/tmna.2021.034","DOIUrl":"https://doi.org/10.12775/tmna.2021.034","url":null,"abstract":"<jats:p />","PeriodicalId":23130,"journal":{"name":"Topological Methods in Nonlinear Analysis","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2022-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47772652","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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