Opuscula Mathematica
Loading...
ISSN 1232-9274
e-ISSN: 2300-6919
Issue Date
2020
Volume
Vol. 40
Number
No. 5
Description
Journal Volume
Opuscula Mathematica
Vol. 40 (2020)
Projects
Pages
Articles
Oscillatory criteria via linearization of half-linear second order delay differential equations
(Wydawnictwa AGH, 2020) Baculíková, Blanka; Džurina, Jozef
In the paper, we study oscillation of the half-linear second order delay differential equations of the form $\left(r(t)(y'(t))^{\alpha}\right)'+p(t)y^{\alpha}(\tau(t))=0.$ We introduce new monotonic properties of its nonoscillatory solutions and use them for linearization of considered equation which leads to new oscillatory criteria. The presented results essentially improve existing ones.
Existence results for a sublinear second order Dirichlet boundary value problem on the half-line
(Wydawnictwa AGH, 2020) Bouafia, Dahmane; Moussaoui, Toufik
In this paper we study the existence of nontrivial solutions for a boundary value problem on the half-line, where the nonlinear term is sublinear, by using Ekeland's variational principle and critical point theory.
On the nonoscillatory behavior of solutions of three classes of fractional difference equations
(Wydawnictwa AGH, 2020) Grace, Said Rezk; Alzabut, Jehad; Punitha, Sakthivel; Muthulakshmi, Velu; Adıgüzel, Hakan
In this paper, we study the nonoscillatory behavior of three classes of fractional difference equations. The investigations are presented in three different folds. Unlike most existing nonoscillation results which have been established by employing Riccati transformation technique, we employ herein an easily verifiable approach based on the fractional Taylor's difference formula, some features of discrete fractional calculus and mathematical inequalities. The theoretical findings are demonstrated by examples. We end the paper by a concluding remark.
On some extensions of the A-model
(Wydawnictwa AGH, 2020) Juršėnas, Rytis
The A-model for finite rank singular perturbations of class $\mathfrak{H}_{-m-2}\setminus\mathfrak{H}_{-m-1}$, $m \in \mathbb{N}$, is considered from the perspective of boundary relations. Assuming further that the Hilbert spaces $(\mathfrak{H}_n)_{n\in\mathbb{Z}}$ admit an orthogonal decomposition $\mathfrak{H}^-_n \oplus \mathfrak{H}^+_n$, with the corresponding projections satisfying $P^{\pm}_{n+1}\subseteq P^{\pm}_n$, nontrivial extensions in the A-model are constructed for the symmetric restrictions in the subspaces.
Outer independent rainbow dominating functions in graphs
(Wydawnictwa AGH, 2020) Mansouri, Zhila; Mojdeh, Doost Ali
A 2-rainbow dominating function (2-rD function) of a graph $G=(V,E)$ is a function $f:V(G)\rightarrow\{\emptyset,\{1\},\{2\},\{1,2\}\}$ having the property that if $f(x)=\emptyset$, then $f(N(x))=\{1,2\}$. The 2-rainbow domination number $\gamma_{r2}(G)$ is the minimum weight of $\sum_{v\in V(G)}|f(v)|$ taken over all 2-rainbow dominating functions $f$. An outer-independent 2-rainbow dominating function (OI2-rD function) of a graph $G$ is a 2-rD function $f$ for which the set of all $v \in V(G)$ with $f(v)=\emptyset$ is independent. The outer independent 2-rainbow domination number $\gamma_{oir2}(G)$ is the minimum weight of an OI2-rD function of $G$. In this paper, we study the OI2-rD number of graphs. We give the complexity of the problem OI2-rD of graphs and present lower and upper bounds on $\gamma_{oir2}(G)$. Moreover, we characterize graphs with some small or large OI2-rD numbers and we also bound this parameter from above for trees in terms of the order, leaves and the number of support vertices and characterize all trees attaining the bound. Finally, we show that any ordered pair $(a,b)$ is realizable as the vertex cover number and OI2-rD numbers of some non-trivial tree if and only if $a+1\leq b\leq 2a$.