Opuscula Mathematica
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ISSN 1232-9274
e-ISSN: 2300-6919
Issue Date
2018
Volume
Vol. 38
Number
No. 3
Description
Journal Volume
Opuscula Mathematica
Vol. 38 (2018)
Projects
Pages
Articles
Solutions to p(x)-Laplace type equations via nonvariational techniques
(Wydawnictwa AGH, 2018) Avci, Mustafa
In this article, we consider a class of nonlinear Dirichlet problems driven by a Leray-Lions type operator with variable exponent. The main result establishes an existence property by means of nonvariational arguments, that is, nonlinear monotone operator theory and approximation method. Under some natural conditions, we show that a weak limit of approximate solutions is a solution of the given quasilinear elliptic partial differential equation involving variable exponent.
Backward stochastic variational inequalities driven by multidimensional fractional Brownian motion
(Wydawnictwa AGH, 2018) Borkowski, Dariusz; Jańczak-Borkowska, Katarzyna
We study the existence and uniqueness of the backward stochastic variational inequalities driven by $m$-dimensional fractional Brownian motion with Hurst parameters $H_k$ ($k=1,\ldots m$) greater than $1/2$. The stochastic integral used throughout the paper is the divergence type integral.
Improved iterative oscillation tests for first-order deviating differential equations
(Wydawnictwa AGH, 2018) Chatzarakis, George E.; Jadlovská, Irena
In this paper, improved oscillation conditions are established for the oscillation of all solutions of differential equations with non-monotone deviating arguments and nonnegative coefficients. They lead to a procedure that checks for oscillations by iteratively computing $\lim \sup$ and $\lim \inf$ on terms recursively defined on the equation's coefficients and deviating argument. This procedure significantly improves all known oscillation criteria. The results and the improvement achieved over the other known conditions are illustrated by two examples, numerically solved in MATLAB.
Forbidden configurations for hypohamiltonian graphs
(Wydawnictwa AGH, 2018) Fabrici, Igor; Madaras, Tomáš; Timková, Mária
A graph $G$ is called hypohamiltonian if $G$ is not hamiltonian, but $G-x$ is hamiltonian for each vertex $x$ of $G$. We present a list of 331 forbidden configurations which do not appear in hypohamiltonian graphs.
On expansive and anti-expansive tree maps
(Wydawnictwa AGH, 2018) Kozerenko, Sergìj Oleksandrovič
With every self-map on the vertex set of a finite tree one can associate the directed graph of a special type which is called the Markov graph. Expansive and anti-expansive tree maps are two extremal classes of maps with respect to the number of loops in their Markov graphs. In this paper we prove that a tree with at least two vertices has a perfect matching if and only if it admits an expansive cyclic permutation of its vertices. Also, we show that for every tree with at least three vertices there exists an expansive map with a weakly connected (strongly connected provided the tree has a perfect matching) Markov graph as well as anti-expansive map with a strongly connected Markov graph.