Opuscula Mathematica
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ISSN 1232-9274
e-ISSN: 2300-6919
Issue Date
2023
Volume
Vol. 43
Number
No. 5
Description
Journal Volume
Opuscula Mathematica
Vol. 43 (2023)
Projects
Pages
Articles
A viability result for Carathéodory non-convex differential inclusion in Banach spaces
(Wydawnictwa AGH, 2023) Charradi, Nabil; Sajid, Saïd
This paper deals with the existence of solutions to the following differential inclusion: $\dot{x}(t)\in F(t,x(t))$ a.e. on $[0,T[$ and $x(t) \in K$, for all $t \in [0,T]$, where $F: [0, T]\times K \rightarrow 2^E$ is a Carathéodory multifunction and $K$ is a closed subset of a separable Banach space $E$.
Volterra integral operators on a family of Dirichlet-Morrey spaces
(Wydawnictwa AGH, 2023) Hu, Lian; Liu, Xiaosong
A family of Dirichlet-Morrey spaces $\mathcal{D}_{\lambda,K}$ of functions analytic in the open unit disk $\mathbb{D}$ are defined in this paper. We completely characterize the boundedness of the Volterra integral operators $T_g$, $I_g$ and the multiplication operator $M_g$ on the space $\mathcal{D}_{\lambda,K}$. In addition, the compactness and essential norm of the operators $T_g$ and $I_g$ on $\mathcal{D}_{\lambda,K}$ are also investigated.
One boundary value problem including a spectral parameter in all boundary conditions
(Wydawnictwa AGH, 2023) Kabataş, Ayşe
In this paper, asymptotic formulae for solutions and Green's function of a boundary value problem are investigated when the equation and the boundary conditions contain a spectral parameter.
The existence of bipartite almost self-complementary 3-uniform hypergraphs
(Wydawnictwa AGH, 2023) Kamble, Lata N.; Deshpande, Charusheela M.; Athawale, Bhagyashri Parag
An almost self-complementary 3-uniform hypergraph on $n$ vertices exists if and only if $n$ is congruent to 3 modulo 4 A hypergraph $H$ with vertex set $V$ and edge set $E$ is called bipartite if $V$ can be partitioned into two subsets $V_1$ and $V_2$ such that $e \cap V_{1} \neq \emptyset$ and $e \cap V_{2} \neq \emptyset$ for any $e \in E$. A bipartite self-complementary 3-uniform hypergraph $H$ with partition $(V_{1},V_{2})$ of the vertex set $V$ such that $|V_{1}|=m$ and $|V_{2}|=n$ exists if and only if either (i) $m=n$ or (ii) $m \neq n$ and either $m$ or $n$ is congruent to 0 modulo 4 or (iii) $m \neq n$ and both $m$ and $n$ are congruent to 1 or 2 modulo 4. In this paper we define a bipartite almost self-complementary 3-uniform hypergraph $H$ with partition $(V_{1},V_{2})$ of a vertex set $V$ such that $|V_{1}|=m$ and $|V_{2}|=n$ and find the conditions on $m$ and $n$ for a bipartite 3-uniform hypergraph $H$ to be almost self-complementary. We also prove the existence of bi-regular bipartite almost self-complementary 3-uniform hypergraphs.
Radial solutions for nonlinear elliptic equation with nonlinear nonlocal boundary conditions
(Wydawnictwa AGH, 2023) Kossowski, Igor
In this article, we prove existence of radial solutions for a nonlinear elliptic equation with nonlinear nonlocal boundary conditions. Our method is based on some fixed point theorem in a cone.