Bukovinian Mathematical Journal最新文献_第9页

ON A TWO-POINT BOUNDARY VALUE PROBLEM FOR A SYSTEM OF DIFFERENTIAL EQUATIONS WITH MANY TRANSFORMED ARGUMENTS 具有多变换参数的微分方程组两点边值问题

Bukovinian Mathematical Journal Pub Date : 1900-01-01 DOI: 10.31861/bmj2021.01.24

M. Filipchuk

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INVERSE SOURCE PROBLEM FOR A SEMILINEAR FRACTIONAL DIFFUSION-WAVE EQUATION UNDER A TIME-INTEGRAL CONDITION 时间积分条件下半线性分数阶扩散波方程的逆源问题

Bukovinian Mathematical Journal Pub Date : 1900-01-01 DOI: 10.31861/bmj2022.02.11

H. Lopushanska

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THE MAXIMUM PRINCIPLE FOR THE EQUATION OF LOCAL FLUCTUATIONS OF RIESZ GRAVITATIONAL FIELDS OF PURELY FRACTIONAL ORDER 纯分数阶riesz引力场局部涨落方程的极大值原理

Bukovinian Mathematical Journal Pub Date : 1900-01-01 DOI: 10.31861/bmj2021.02.06

V. Litovchenko

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STRONG CONTINUITY OF FUNCTIONS FROM TWO VARIABLES 两变量函数的强连续性

Bukovinian Mathematical Journal Pub Date : 1900-01-01 DOI: 10.31861/bmj2021.01.19

V. Nesterenko, V. Lazurko

{"title":"STRONG CONTINUITY OF FUNCTIONS FROM TWO VARIABLES","authors":"V. Nesterenko, V. Lazurko","doi":"10.31861/bmj2021.01.19","DOIUrl":"https://doi.org/10.31861/bmj2021.01.19","url":null,"abstract":"The concept of continuity in a strong sense for the case of functions with values in metric spaces is studied. The separate and joint properties of this concept are investigated, and several results by Russell are generalized.\u0000\u0000A function $f:X times Y to Z$ is strongly continuous with respect to $x$ /$y$/ at a point ${(x_0, y_0)in X times Y}$ provided for an arbitrary $varepsilon> 0$ there are neighborhoods $U$ of $x_0$ in $X$ and $V$ of $y_0$ in $Y$ such that $d(f(x, y), f(x_0, y)) <varepsilon$ /$d((x, y), f (x, y_0))<varepsilon$/ for all $x in U$ and $y in V$. A function $f$ is said to be strongly continuous with respect to $x$ /$y$/ if it is so at every point $(x, y)in X times Y$.\u0000\u0000Note that, for a real function of two variables, the notion of continuity in the strong sense with respect to a given variable and the notion of strong continuity with respect to the same variable are equivalent.\u0000\u0000In 1998 Dzagnidze established that a real function of two variables is continuous over a set of variables if and only if it is continuous in the strong sense with respect to each of the variables.\u0000\u0000Here we transfer this result to the case of functions with values in a metric space: if $X$ and $Y$ are topological spaces, $Z$ a metric space and a function $f:X times Y to Z$ is strongly continuous with respect to $y$ at a point $(x_0, y_0) in X times Y$, then the function $f$ is jointly continuous if and only if $f_{y}$ is continuous for all $yin Y$.\u0000\u0000It is obvious that every continuous function $f:X times Y to Z$ is strongly continuous with respect to $x$ and $y$, but not vice versa. On the other hand, the strong continuity of the function $f$ with respect to $x$ or $y$ implies the continuity of $f$ with respect to $x$ or $y$, respectively. Thus, strongly separately continuous functions are separately continuous.\u0000\u0000Also, it is established that for topological spaces $X$ and $Y$ and a metric space $Z$ a function $f:X times Y to Z$ is jointly continuous if and only if the function $f$ is strongly continuous with respect to $x$ and $y$.","PeriodicalId":196726,"journal":{"name":"Bukovinian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123542516","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

ASYMPTOTIC REPRESENTATIONS OF SOLUTIONS WITH SLOWLY VARYING DERIVATIVES OF THE SECOND ORDER DIFFERENTIAL EQUATIONS WITH THE PRODUCT OF DIFFERENT TYPES OF NONLINEARITIES 二阶微分方程与不同类型非线性乘积的缓变导数解的渐近表示

Bukovinian Mathematical Journal Pub Date : 1900-01-01 DOI: 10.31861/bmj2020.02.081

O. Chepok

{"title":"ASYMPTOTIC REPRESENTATIONS OF SOLUTIONS WITH SLOWLY VARYING DERIVATIVES OF THE SECOND ORDER DIFFERENTIAL EQUATIONS WITH THE PRODUCT OF DIFFERENT TYPES OF NONLINEARITIES","authors":"O. Chepok","doi":"10.31861/bmj2020.02.081","DOIUrl":"https://doi.org/10.31861/bmj2020.02.081","url":null,"abstract":"Signi cantly nonlinear non-autonomous di erential equations have begun to appear in practice from the second half of the nineteenth century in the study of real physical processes in atomic and nuclear physics, and also in astrophysics. The di erential equation, that contains in its right part the product of regularly and rapidly varying nonlinearities of an unknown function and its rst-order derivative is considered in the paper. Partial cases of such equations arise, rst of all, in the theory of combustion and in the theory of plasma. The rst important results on the asymptotic behavior of solutions of such equations have been obtained for a second-order di erential equation, that contains the product of power and exponential nonlinearities in its right part. For, no such equations have been obtained before. According to this, the study of the asymptotic behavior of solutions of nonlinear di erential equations of the second order of general case, that contain the product of regularly and rapidly varying nonlinearities as the argument tends either to zero or to in nity, is actual not only from the theoretical but also from the practical point of view. The asymptotic representations, as well as the necessary and su cient conditions of the existence of Pω(Y0, Y1,±∞)-solutions of such equations are investigated in the paper. This class of solutions is the one of the most di cult of studying due to the fact that, by the a priori properties of the functions of the class, their second-order derivatives aren't explicitly expressed through the rst-order derivative. The results obtained in this article supplement the previously obtained results for Pω(Y0, Y1,±∞)-solutions of the investigated equation concerning the su cient conditions of their existence and quantity.","PeriodicalId":196726,"journal":{"name":"Bukovinian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130467588","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 fawar problem and problem of kolmogorov-nikolsky solved by V.K. Dzyadyk 论法瓦尔问题和季亚季克解的柯尔莫哥罗夫-尼科夫斯基问题

Bukovinian Mathematical Journal Pub Date : 1900-01-01 DOI: 10.31861/bmj2019.01.048

P. Zaderei, S. Ivasyshen, N. Zaderei, G. Nefodova

引用次数: 0

DELAY MODELING OF MATHEMATICAL MODELS OF BIOLOGY AND IMMUNOLOGY 生物学和免疫学数学模型的延迟建模

Bukovinian Mathematical Journal Pub Date : 1900-01-01 DOI: 10.31861/bmj2021.02.07

T. Lunyk, I. Cherevko

引用次数: 0

A MULTIPOINT IN-TIME PROBLEM FOR THE 2b-PARABOLIC EQUATION WITH DEGENERATION 具有退化的2b-抛物型方程的多点时间问题

Bukovinian Mathematical Journal Pub Date : 1900-01-01 DOI: 10.31861/bmj2022.02.18

I. Pukalskyy, B. Yashan

{"title":"A MULTIPOINT IN-TIME PROBLEM FOR THE 2b-PARABOLIC EQUATION WITH DEGENERATION","authors":"I. Pukalskyy, B. Yashan","doi":"10.31861/bmj2022.02.18","DOIUrl":"https://doi.org/10.31861/bmj2022.02.18","url":null,"abstract":"In recent decades, special attention has been paid to problems with nonlocal conditions for partial differential equations. Such interest in such problems is due to both the needs of the general therapy of boundary value problems and their rich practical application (the process of diffusion, oscillations, salt and moisture transport in soils, plasma physics, mathematical\u0000biology, etc.).\u0000A multipoint in-time problem for a nonuniformly 2b-parabolic equation with degeneracy is studied. The coefficients of the parabolic equation of order 2b allow for power singularities of arbitrary order both in the time and spatial variables at some set of points. Solutions of auxiliary problems with smooth coefficients are studied to solve the given problem. Using a priori estimates, inequalities are established for solving problems and their derivatives in special Hölder spaces. Using the theorems of Archel and Riess, a convergent sequence is distinguished from a compact sequence of solutions of auxiliary problems, the limiting value of which will be the solution of the given problem. Estimates of the solution of the multipoint time problem for the 2b-parabolic equation are established in Hölder spaces with power-law weights. The order of the power weight is determined by the order of degeneracy of the coefficients of the groups of higher terms and the power features of the coefficients of the lower terms of the parabolic equation. With certain restrictions on the right-hand side of the equation, an integral image of the solution to the given problem is obtained.","PeriodicalId":196726,"journal":{"name":"Bukovinian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115313220","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