Opuscula Mathematica
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ISSN 1232-9274
e-ISSN: 2300-6919
Issue Date
2012
Volume
Vol. 32
Number
No. 3
Description
Journal Volume
Opuscula Mathematica
Vol. 32 (2012)
Projects
Pages
Articles
White noise based stochastic calculus associated with a class of Gaussian processes
(2012) Alpay, Daniel; Attia, Haim; Levanony, David
Using the white noise space setting, we define and study stochastic integrals with respect to a class of stationary increment Gaussian processes. We focus mainly on continuous functions with values in the Kondratiev space of stochastic distributions, where use is made of the topology of nuclear spaces. We also prove an associated Ito formula.
Trees whose 2-domination subdivision number is 2
(2012) Atapour, Maryam; Sheikholeslami, Seyed Mahmoud; Khodkar, Abdollah
A set S of vertices in a graph $G=(V,E)$ is a $2$-dominating set if every vertex of $V\setminus S$ is adjacent to at least two vertices of $S$. The $2$-domination number of a graph $G$, denoted by $\gamma_2(G)$, is the minimum size of a $2$-dominating set of $G$. The $2$-domination subdivision number $sd_{\gamma_2}(G)$ is the minimum number of edges that must be subdivided (each edge in $G$ can be subdivided at most once) in order to increase the $2$-domination number. The authors have recently proved that for any tree $T$ of order at least $3$, $1 \leq sd_{\gamma_2}(T)\leq 2$. In this paper we provide a constructive characterization of the trees whose $2$-domination subdivision number is $2$.
Existence result for hemivariational inequality involving p(x)-Laplacian
(2012) Barnaś, Sylwia
In this paper we study the nonlinear elliptic problem with $p(x)$-Laplacian (hemivariational inequality). We prove the existence of a nontrivial solution. Our approach is based on critical point theory for locally Lipschitz functionals due to Chang [J. Math. Anal. Appl. 80 (1981), 102-129].
Stepanov-like C(n)-pseudo almost automorphy and applications to some nonautonomous higher-order differential equations
(2012) Diagana, Toka; Nelson, Valerie; N'Guérékata, Gaston Mandata
In this paper we introduce and study a new concept called Stepanov-like $C^{(n)}$-pseudo almost automorphy, which generalizes in a natural fashion both the notions of $C^{(n)}$-pseudo almost periodicity and that of $C^{(n)}$-pseudo almost automorphy recently introduced in the literature by the authors. Basic properties of these new functions are investigated. Furthermore, we study and obtain the existence of $C^{(N+m)}$-pseudo almost automorphic solutions to some nonautonomous higher-order systems of differential equations with Stepanov-like $C^{(m)}$-pseudo almost automorphic coefficients.
On the existence of three solutions for quasilinear elliptic problem
(2012) Goncerz, Paweł
We consider a quasilinear elliptic problem of the type $-\Delta_p u = \lambda (f(u)+\mu g(u))$ in $\Omega$, $u|_{\partial \Omega} =0$, where $\Omega \in \mathbb{R}^N$ is an open and bounded set, $f$, $g$ are continuous real functions on $\mathbb{R}$ and $\lambda , \mu \in \mathbb{R}$. We prove the existence of at least three solutions for this problem using the so called three critical points theorem due to Ricceri.