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Entire solutions for some critical equations in the Heisenberg group 海森堡群中某些关键方程的全解
IF 1
Opuscula Mathematica Pub Date : 2022-01-01 DOI: 10.7494/opmath.2022.42.2.279
P. Pucci, Letizia Temperini
{"title":"Entire solutions for some critical equations in the Heisenberg group","authors":"P. Pucci, Letizia Temperini","doi":"10.7494/opmath.2022.42.2.279","DOIUrl":"https://doi.org/10.7494/opmath.2022.42.2.279","url":null,"abstract":"We complete the study started in the paper [P. Pucci, L.Temperini, On the concentration-compactness principle for Folland-Stein spaces and for fractional horizontal Sobolev spaces, Math. Eng. 5 (2023), Paper no. 007], giving some applications of its abstract results to get existence of solutions of certain critical equations in the entire Heinseberg group. In particular, different conditions for existence are given for critical horizontal (p)-Laplacian equations.","PeriodicalId":45563,"journal":{"name":"Opuscula Mathematica","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71342476","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}
引用次数: 5
Strong consistency of the local linear relative regression estimator for censored data 截尾数据局部线性相对回归估计量的强相合性
IF 1
Opuscula Mathematica Pub Date : 2022-01-01 DOI: 10.7494/opmath.2022.42.6.805
Feriel Bouhadjera, E. Said
{"title":"Strong consistency of the local linear relative regression estimator for censored data","authors":"Feriel Bouhadjera, E. Said","doi":"10.7494/opmath.2022.42.6.805","DOIUrl":"https://doi.org/10.7494/opmath.2022.42.6.805","url":null,"abstract":"In this paper, we combine the local linear approach to the relative error regression estimation method to build a new estimator of the regression operator when the response variable is subject to random right censoring. We establish the uniform almost sure consistency with rate over a compact set of the proposed estimator. Numerical studies, firstly on simulated data, then on a real data set concerning the death times of kidney transplant patients, were conducted. These practical studies clearly show the superiority of the new estimator compared to competitive estimators.","PeriodicalId":45563,"journal":{"name":"Opuscula Mathematica","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71342887","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}
引用次数: 0
Solution of the boundary value problem of heat conduction in a cone 锥内热传导边值问题的求解
IF 1
Opuscula Mathematica Pub Date : 2022-01-01 DOI: 10.7494/opmath.2022.42.1.75
M. Ramazanov, M. Jenaliyev, N. Gulmanov
{"title":"Solution of the boundary value problem of heat conduction in a cone","authors":"M. Ramazanov, M. Jenaliyev, N. Gulmanov","doi":"10.7494/opmath.2022.42.1.75","DOIUrl":"https://doi.org/10.7494/opmath.2022.42.1.75","url":null,"abstract":"In the paper we consider the boundary value problem of heat conduction in a non-cylindrical domain, which is an inverted cone, i.e. in the domain degenerating into a point at the initial moment of time. In this case, the boundary conditions contain a derivative with respect to the time variable; in practice, problems of this kind arise in the presence of the condition of the concentrated heat capacity. We prove a theorem on the solvability of a boundary value problem in weighted spaces of essentially bounded functions. The issues of solvability of the singular Volterra integral equation of the second kind, to which the original problem is reduced, are studied. We use the Carleman-Vekua method of equivalent regularization to solve the obtained singular Volterra integral equation.","PeriodicalId":45563,"journal":{"name":"Opuscula Mathematica","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71342072","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}
引用次数: 2
Blowup phenomena for some fourth-order strain wave equations at arbitrary positive initial energy level 一些四阶应变波方程在任意正初始能级上的爆破现象
IF 1
Opuscula Mathematica Pub Date : 2022-01-01 DOI: 10.7494/opmath.2022.42.2.219
Q. Lin, Yong-bing Luo
{"title":"Blowup phenomena for some fourth-order strain wave equations at arbitrary positive initial energy level","authors":"Q. Lin, Yong-bing Luo","doi":"10.7494/opmath.2022.42.2.219","DOIUrl":"https://doi.org/10.7494/opmath.2022.42.2.219","url":null,"abstract":"In this paper, we study a series of fourth-order strain wave equations involving dissipative structure, which appears in elasto-plastic-microstructure models. By some differential inequalities, we derive the finite time blow up results and the estimates of the upper bound blowup time with arbitrary positive initial energy. We also discuss the influence mechanism of the linear weak damping and strong damping on blowup time, respectively.","PeriodicalId":45563,"journal":{"name":"Opuscula Mathematica","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71342302","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}
引用次数: 1
Exponential decay of solutions to a class of fourth-order nonlinear hyperbolic equations modeling the oscillations of suspension bridges 一类模拟悬索桥振动的四阶非线性双曲方程解的指数衰减
IF 1
Opuscula Mathematica Pub Date : 2022-01-01 DOI: 10.7494/opmath.2022.42.2.239
Yang Liu, Chao Yang
{"title":"Exponential decay of solutions to a class of fourth-order nonlinear hyperbolic equations modeling the oscillations of suspension bridges","authors":"Yang Liu, Chao Yang","doi":"10.7494/opmath.2022.42.2.239","DOIUrl":"https://doi.org/10.7494/opmath.2022.42.2.239","url":null,"abstract":"This paper is concerned with a class of fourth-order nonlinear hyperbolic equations subject to free boundary conditions that can be used to describe the nonlinear dynamics of suspension bridges.","PeriodicalId":45563,"journal":{"name":"Opuscula Mathematica","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71342315","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}
引用次数: 0
On Ambarzumian type theorems for tree domains 关于树域的Ambarzumian型定理
IF 1
Opuscula Mathematica Pub Date : 2022-01-01 DOI: 10.7494/opmath.2022.42.3.427
V. Pivovarchik
{"title":"On Ambarzumian type theorems for tree domains","authors":"V. Pivovarchik","doi":"10.7494/opmath.2022.42.3.427","DOIUrl":"https://doi.org/10.7494/opmath.2022.42.3.427","url":null,"abstract":"It is known that the spectrum of the spectral Sturm-Liouville problem on an equilateral tree with (generalized) Neumann's conditions at all vertices uniquely determines the potentials on the edges in the unperturbed case, i.e. case of the zero potentials on the edges (Ambarzumian's theorem). This case is exceptional, and in general case (when the Dirichlet conditions are imposed at some of the pendant vertices) even two spectra of spectral problems do not determine uniquely the potentials on the edges. We consider the spectral Sturm-Liouville problem on an equilateral tree rooted at its pendant vertex with (generalized) Neumann conditions at all vertices except of the root and the Dirichlet condition at the root. In this case Ambarzumian's theorem can't be applied. We show that if the spectrum of this problem is unperturbed, the spectrum of the Neumann-Dirichlet problem on the root edge is also unperturbed and the spectra of the problems on the complimentary subtrees with (generalized) Neumann conditions at all vertices except the subtrees' roots and the Dirichlet condition at the subtrees' roots are unperturbed then the potential on each edge of the tree is 0 almost everywhere.","PeriodicalId":45563,"journal":{"name":"Opuscula Mathematica","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71342035","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}
引用次数: 2
On oscillatory behaviour of third-order half-linear dynamic equations on time scales 时间尺度上三阶半线性动力学方程的振荡特性
IF 1
Opuscula Mathematica Pub Date : 2022-01-01 DOI: 10.7494/opmath.2022.42.6.849
S. Grace, G. N. Chhatria
{"title":"On oscillatory behaviour of third-order half-linear dynamic equations on time scales","authors":"S. Grace, G. N. Chhatria","doi":"10.7494/opmath.2022.42.6.849","DOIUrl":"https://doi.org/10.7494/opmath.2022.42.6.849","url":null,"abstract":"In this work, we study the oscillation and asymptotic behaviour of third-order nonlinear dynamic equations on time scales. The findings are obtained using an integral criterion as well as a comparison theorem with the oscillatory properties of a first-order dynamic equation. As a consequence, we give conditions which guarantee that all solutions to the aforementioned problem are only oscillatory, different from any other result in the literature. We propose novel oscillation criteria that improve, extend, and simplify existing ones in the literature. The results are associated with a numerical example. We point out that the results are new even for the case (mathbb{T}=mathbb{R}) or (mathbb{T}=mathbb{Z}).","PeriodicalId":45563,"journal":{"name":"Opuscula Mathematica","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71342499","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}
引用次数: 0
Critical cases in neutral functional differential equations, arising from hydraulic engineering 中性泛函微分方程的临界情况，由水利工程引起
IF 1
Opuscula Mathematica Pub Date : 2022-01-01 DOI: 10.7494/opmath.2022.42.4.605
Vladimir R�svan
{"title":"Critical cases in neutral functional differential equations, arising from hydraulic engineering","authors":"Vladimir R�svan","doi":"10.7494/opmath.2022.42.4.605","DOIUrl":"https://doi.org/10.7494/opmath.2022.42.4.605","url":null,"abstract":"This paper starts from several applications described by initial/boundary value problems for (1D) (time and one space variable) hyperbolic partial differential equations whose basic properties and stability of equilibria are studied throughout the same properties for certain associated neutral functional differential equations. It is a common fact that asymptotic stability for neutral functional differential equations is normally obtained under the assumption of asymptotic stability of the difference operator associated to the aforementioned neutral functional differential equations. However the physically meaningful applications presented in the paper have the associated difference operator(s) in critical cases (their stability is, generally speaking, non-asymptotic). Consequently the stability of the considered application models is either non-asymptotic or fragile (in a sense introduced in the paper). The models represent an overview gathered from various fields, processed here in order to emphasize the associated neutral functional differential equations which, consequently, are a challenge to the usual approaches. In the concluding part there are suggested possible ways to overcome these difficulties.","PeriodicalId":45563,"journal":{"name":"Opuscula Mathematica","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71342598","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}
引用次数: 2
Discrete spectrum of zero order pseudodifferential operators 零阶伪微分算子的离散谱
IF 1
Opuscula Mathematica Pub Date : 2021-12-10 DOI: 10.7494/opmath.2023.43.2.247
G. Rozenblum
{"title":"Discrete spectrum of zero order pseudodifferential operators","authors":"G. Rozenblum","doi":"10.7494/opmath.2023.43.2.247","DOIUrl":"https://doi.org/10.7494/opmath.2023.43.2.247","url":null,"abstract":"For a class of zero order pseudodifferential operators we find the asymptotics of eigenvalues converging to a non-isolated tip of the essential spectrum.","PeriodicalId":45563,"journal":{"name":"Opuscula Mathematica","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48883595","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}
引用次数: 2
The Krein-von Neumann extension of a regular even order quasi-differential operator 正则偶阶拟微分算子的Krein-von Neumann扩展
IF 1
Opuscula Mathematica Pub Date : 2021-08-28 DOI: 10.7494/opmath.2021.41.6.805
Minsung Cho, Seth Hoisington, Roger Nichols, Brian Udall
{"title":"The Krein-von Neumann extension of a regular even order quasi-differential operator","authors":"Minsung Cho, Seth Hoisington, Roger Nichols, Brian Udall","doi":"10.7494/opmath.2021.41.6.805","DOIUrl":"https://doi.org/10.7494/opmath.2021.41.6.805","url":null,"abstract":"We characterize by boundary conditions the Krein-von Neumann extension of a strictly positive minimal operator corresponding to a regular even order quasi-differential expression of Shin-Zettl type. The characterization is stated in terms of a specially chosen basis for the kernel of the maximal operator and employs a description of the Friedrichs extension due to Möller and Zettl.","PeriodicalId":45563,"journal":{"name":"Opuscula Mathematica","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44207299","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}
引用次数: 0
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