Pub Date : 2018-09-01DOI: 10.15393/J3.ART.2018.5330
A. Losev, E. Mazepa
We study questions of existence and belonging to a given functional class of solutions of the inhomogeneous elliptic equations ∆u − c(x)u = g(x), where c(x) > 0, g(x) are Hölder fuctions on a noncompact Riemannian manifold M without boundary. In this work we develop an approach to evaluation of solutions to boundary-value problems for linear and quasilinear equations of the elliptic type on arbitrary noncompact Riemannian manifolds. Our technique is essentially based on an approach from the papers by E. A. Mazepa and S. A. Korol’kov connected with an introduction of equivalency classes of functions and representations. We investigate the relationship between the existence of solutions of this equation on M and outside some compact set B ⊂ M with the same growth "at infinity".
研究了一类非齐次椭圆方程(∆u−c(x)u = g(x)解的存在性问题，其中c(x) > 0, g(x)是无界非紧黎曼流形M上的Hölder函数。本文提出了一种求任意非紧黎曼流形上椭圆型线性方程和拟线性方程边值问题解的方法。我们的技术本质上是基于E. A. Mazepa和S. A. Korol 'kov论文中的一种方法，该方法与函数和表示的等价类的介绍有关。我们研究了该方程在M上与具有相同增长“在无穷远处”的紧集B∧M外解的存在性之间的关系。
{"title":"On solvability of the boundary value problems for the inhomogeneous elliptic equations on noncompact Riemannian manifolds","authors":"A. Losev, E. Mazepa","doi":"10.15393/J3.ART.2018.5330","DOIUrl":"https://doi.org/10.15393/J3.ART.2018.5330","url":null,"abstract":"We study questions of existence and belonging to a given functional class of solutions of the inhomogeneous elliptic equations ∆u − c(x)u = g(x), where c(x) > 0, g(x) are Hölder fuctions on a noncompact Riemannian manifold M without boundary. In this work we develop an approach to evaluation of solutions to boundary-value problems for linear and quasilinear equations of the elliptic type on arbitrary noncompact Riemannian manifolds. Our technique is essentially based on an approach from the papers by E. A. Mazepa and S. A. Korol’kov connected with an introduction of equivalency classes of functions and representations. We investigate the relationship between the existence of solutions of this equation on M and outside some compact set B ⊂ M with the same growth \"at infinity\".","PeriodicalId":41813,"journal":{"name":"Problemy Analiza-Issues of Analysis","volume":"92 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84054150","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-08-15DOI: 10.15393/j3.art.2019.5210
S. Kalmykov, D. Karp
We establish conditions for the discrete versions of logarithmic concavity and convexity of the higher order regularized basic hypergeometric function with respect simultaneous shift of all its parameters. For a particular case of Heine's basic hypergeometric function we prove logarithmic concavity and convexity with respect to the bottom parameter. We further establish a linearization identity for the generalized Tur'{a}nian formed by a particular case of Heine's basic hypergeometric function. Its $q=1$ case also appears to be new.
{"title":"Inequalities for some basic hypergeometric functions","authors":"S. Kalmykov, D. Karp","doi":"10.15393/j3.art.2019.5210","DOIUrl":"https://doi.org/10.15393/j3.art.2019.5210","url":null,"abstract":"We establish conditions for the discrete versions of logarithmic concavity and convexity of the higher order regularized basic hypergeometric function with respect simultaneous shift of all its parameters. For a particular case of Heine's basic hypergeometric function we prove logarithmic concavity and convexity with respect to the bottom parameter. We further establish a linearization identity for the generalized Tur'{a}nian formed by a particular case of Heine's basic hypergeometric function. Its $q=1$ case also appears to be new.","PeriodicalId":41813,"journal":{"name":"Problemy Analiza-Issues of Analysis","volume":"41 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2018-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75510988","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-08-13DOI: 10.15393/j3.art.2018.5250
V. Kolokoltsov, M. Troeva
In this paper we study the sensitivity of nonlinear stochastic differential equations of McKean-Vlasov type generated by stable-like processes. By using the method of stochastic characteristics, we transfer these equations to the non-stochastic equations with random coefficients thus making it possible to use the results obtained for nonlinear PDE of McKean-Vlasov type generated by stable-like processes in the previous works. The motivation for studying sensitivity of nonlinear McKean-Vlasov SPDEs arises naturally from the analysis of the mean-field games with common noise.
{"title":"Regularity and Sensitivity for McKean-Vlasov Type SPDEs Generated by Stable-like Processes","authors":"V. Kolokoltsov, M. Troeva","doi":"10.15393/j3.art.2018.5250","DOIUrl":"https://doi.org/10.15393/j3.art.2018.5250","url":null,"abstract":"In this paper we study the sensitivity of nonlinear stochastic differential equations of McKean-Vlasov type generated by stable-like processes. By using the method of stochastic characteristics, we transfer these equations to the non-stochastic equations with random coefficients thus making it possible to use the results obtained for nonlinear PDE of McKean-Vlasov type generated by stable-like processes in the previous works. The motivation for studying sensitivity of nonlinear McKean-Vlasov SPDEs arises naturally from the analysis of the mean-field games with common noise.","PeriodicalId":41813,"journal":{"name":"Problemy Analiza-Issues of Analysis","volume":"16 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2018-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86284580","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-06-01DOI: 10.15393/J3.ART.2018.4690
V. V. Volchkov, V. Volchkov
{"title":"A NEW CHARACTERIZATION OF HOLOMORPHIC FUNCTIONS IN THE UNIT DISK","authors":"V. V. Volchkov, V. Volchkov","doi":"10.15393/J3.ART.2018.4690","DOIUrl":"https://doi.org/10.15393/J3.ART.2018.4690","url":null,"abstract":"","PeriodicalId":41813,"journal":{"name":"Problemy Analiza-Issues of Analysis","volume":"2 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87821307","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-06-01DOI: 10.15393/j3.art.2018.4350
Ahmed A. Hamoud, K. Ghadle
{"title":"The Approximate Solutions of Fractional Volterra-Fredholm Integro-Differential Equations by using Analytical Techniques","authors":"Ahmed A. Hamoud, K. Ghadle","doi":"10.15393/j3.art.2018.4350","DOIUrl":"https://doi.org/10.15393/j3.art.2018.4350","url":null,"abstract":"","PeriodicalId":41813,"journal":{"name":"Problemy Analiza-Issues of Analysis","volume":"10 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87775951","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-06-01DOI: 10.15393/j3.art.2018.4370
Feng Qi (祁锋)
{"title":"An Improper Integral, the Beta Function, the Wallis Ratio, and the Catalan Numbers","authors":"Feng Qi (祁锋)","doi":"10.15393/j3.art.2018.4370","DOIUrl":"https://doi.org/10.15393/j3.art.2018.4370","url":null,"abstract":"","PeriodicalId":41813,"journal":{"name":"Problemy Analiza-Issues of Analysis","volume":"23 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76938763","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-06-01DOI: 10.15393/j3.art.2018.4730
S. Ponnusamy, K. Wirths
{"title":"Coefficient problems on the class U(λ)","authors":"S. Ponnusamy, K. Wirths","doi":"10.15393/j3.art.2018.4730","DOIUrl":"https://doi.org/10.15393/j3.art.2018.4730","url":null,"abstract":"","PeriodicalId":41813,"journal":{"name":"Problemy Analiza-Issues of Analysis","volume":"2011 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86324300","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-06-01DOI: 10.15393/J3.ART.2018.4830
J. E. Kim
{"title":"The corresponding Cauchy-Riemann system for dual quaternion-valued functions","authors":"J. E. Kim","doi":"10.15393/J3.ART.2018.4830","DOIUrl":"https://doi.org/10.15393/J3.ART.2018.4830","url":null,"abstract":"","PeriodicalId":41813,"journal":{"name":"Problemy Analiza-Issues of Analysis","volume":"20 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90495910","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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