Opuscula Mathematica
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ISSN 1232-9274
e-ISSN: 2300-6919
Issue Date
2017
Volume
Vol. 37
Number
No. 6
Description
Journal Volume
Opuscula Mathematica
Vol. 37 (2017)
Projects
Pages
Articles
On the Steklov problem involving the p(x)-Laplacian with indefinite weight
(Wydawnictwa AGH, 2017) Ali, Khaled Ben; Ghanmi, Abdeljabbar; Kefi, Khaled
Under suitable assumptions, we study the existence of a weak nontrivial solution for the following Steklov problem involving the $p(x)$-Laplacian $\begin{cases}\Delta_{p(x)}u=a(x)|u|^{p(x)-2}u \quad \text{in }\Omega, \\ |\nabla u|^{p(x)-2}\frac{\partial u}{\partial \nu}=\lambda V(x)|u|^{q(x)-2}u \quad \text{on }\partial \Omega.\end{cases}$
Our approach is based on min-max method and Ekeland's variational principle.
The second Cushing-Henson conjecture for the Beverton-Holt q-difference equation
(Wydawnictwa AGH, 2017) Bohner, Martin; Streipert, Sabrina H.
In this paper, we study the second Cushing-Henson conjecture for the Beverton-Holt difference equation with periodic inherent growth rate and periodic carrying capacity in the quantum calculus setting. We give a short summary of recent results regarding the Beverton-Holt difference and $q$-difference equation and introduce the theory of quantum calculus briefly. Next, we analyze the second Cushing-Henson conjecture. We extend recent studies in [The Beverton-Holt q-difference equation with periodic growth rate, Difference Equations, Discrete Dynamical Systems, and Applications, Springer-Verlag, Berlin, Heidelberg, New York, 2015, pp. 3-14] and state a modified formulation of the second Cushing-Henson conjecture for the Beverton-Holt $q$-difference equation as a generalization of existing formulations.
A direct approach to linear-quadratic stochastic control
(Wydawnictwa AGH, 2017) Duncan, Tyrone E.; Pasik-Duncan, Bozenna
A direct approach is used to solve some linear-quadratic stochastic control problems for Brownian motion and other noise processes. This direct method does not require solving Hamilton-Jacobi-Bellman partial differential equations or backward stochastic differential equations with a stochastic maximum principle or the use of a dynamic programming principle. The appropriate Riccati equation is obtained as part of the optimization problem. The noise processes can be fairly general including the family of fractional Brownian motions.
Ideals with linear quotients in Segre products
(Wydawnictwa AGH, 2017) Failla, Gioia
We establish that the Segre product between a polynomial ring on a field $K$ in m variables and the second squarefree Veronese subalgebra of a polynomial ring on $K$ in n variables has the intersection degree equal to three. We describe a class of monomial ideals of the Segre product with linear quotients.
Oscillatory and asymptotic behavior of a third-order nonlinear neutral differential equation
(Wydawnictwa AGH, 2017) Graef, John R.; Tunҫ, Ercan; Grace, Said R.
This paper discusses oscillatory and asymptotic properties of solutions of a class of third-order nonlinear neutral differential equations. Some new sufficient conditions for a solution of the equation to be either oscillatory or to converges to zero are presented. The results obtained can easily be extended to more general neutral differential equations as well as to neutral dynamic equations on time scales. Two examples are provided to illustrate the results.