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Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Wokół liczb i szeregów harmonicznych

100%
Wiśniewski D.
Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
|
2015
|
tom 7
99-109
PL
The harmonic series is one of the most celebrated infinite series ofmathematics. From a pedagogical point of view, the harmonic series providesa wealth of opportunities. Applications such as Gabriel’s wedding cake andEuler’s proof of the divergence of prime numbers can lead to some verynice discussions. The main idea of this article is to survey some of unusual,insightful and inspiring divergence proofs. First of all, this article is addressedat first-year calculus students.
2
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The Behaviour of Weak Solutions of Boundary Value Problems for Linear Elliptic Second Order Equations in Unbounded Cone-Like Domains

100%
Wiśniewski D.
Annales Mathematicae Silesianae
|
2016
|
tom 30
|
nr 1
203-217
EN
We investigate the behaviour of weak solutions of boundary value problems (Dirichlet, Neumann, Robin and mixed) for linear elliptic divergence second order equations in domains extending to infinity along a cone. We find an exponent of the solution decreasing rate: we derive the estimate of the weak solution modulus for our problems near the infinity under assumption that leading coefficients of the equations do not satisfy the Dini-continuity condition.
3
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Metoda Frobeniusa, czyli o rozwiązywaniu pewnej klasy równań różniczkowych

64%
Wiśniewski D., Żyjewski K.
Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam Mathematicae Pertinentia
|
2016
|
tom 8
139-158
PL
The article is a comprehensive research paper which provides theoreticalas well as practical aspects of the Ferdinand George Frobenius method.This method is based on seeking infinite series solutions for certainclass of differential equations. It is a generalization of the power series methodand allows us to solve the differential equations at least near somesingular points.
4
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An integro-differential inequality related to the smallest positive eigenvalue ofp(x)-Laplacian Dirichlet problem

64%
Wiśniewski D., Bodzioch M.
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
|
2016
|
tom 15
EN
We consider the eigenvalue problem for the p(x)-Laplace-Beltrami operator on the unit sphere. We prove same integro-differential inequalities related to the smallest positive eigenvalue of this problem.
5
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Boundary value problems for quasi-linear elliptic second order equations in unbounded cone-like domains

64%
Borsuk M., Wiśniewski D.
Open Mathematics
|
2012
|
tom 10
|
nr 6
2051-2072
EN
We study the behaviour of weak solutions (as well as their gradients) of boundary value problems for quasi-linear elliptic divergence equations in domains extending to infinity along a cone.
6
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Comments on behaviour of solutions of elliptic quasi-linear problems in a neighbourhood of boundary singularities

51%
Bodzioch M., Wiśniewski D., Żyjewski K.
Open Mathematics
|
2017
|
tom 15
|
nr 1
667-678
EN
We have investigated the behaviour of solutions of elliptic quasi-linear problems in a neighbourhood of boundary singularities in bounded and unbounded domains. We found exponents of the solution’s decreasing rate near the boundary singularities.
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