University of West Bohemia

About: University of West Bohemia is a education organization based out in Pilsen, Czechia. It is known for research contribution in the topics: Sputter deposition & Band gap. The organization has 2587 authors who have published 7207 publications receiving 78537 citations. The organization is also known as: Západočeská Univerzita v Plzni & ZČU.

Remarks on minimizers for ( p , q )-Laplace equations with two parameters

Abstract: We study in detail the existence, nonexistence and behavior of global minimizers, ground states and corresponding energy levels of the \begin{document}$(p, q)$\end{document} -Laplace equation \begin{document}$-Δ_p u -Δ_q u = α |u|^{p-2}u + β |u|^{q-2}u$\end{document} in a bounded domain $Ω \subset \mathbb{R}^N$ under zero Dirichlet boundary condition, where \begin{document}$p > q > 1$\end{document} and \begin{document}$α, β ∈ \mathbb{R}$\end{document} . A curve on the \begin{document}$(α, β)$\end{document} -plane which allocates a set of the existence of ground states and the multiplicity of positive solutions is constructed. Additionally, we show that eigenfunctions of the p-and q-Laplacians under zero Dirichlet boundary condition are linearly independent.

A Hybrid Technique Based on a Genetic Algorithm for Fuzzy Multiobjective Problems in 5G, Internet of Things, and Mobile Edge Computing

Abstract: Emerging commucation technologies, such as mobile edge computing (MEC), Internet of Things (IoT), and fifth-generation (5G) broadband cellular networks, have recently drawn a great deal of interest. Therefore, numerous multiobjective optimization problems (MOOP) associated with the aforementioned technologies have arisen, for example, energy consumption, cost-effective edge user allocation (EUA), and efficient scheduling. Accordingly, the formularization of these problems through fuzzy relation equations (FRE) should be taken into consideration as a capable approach to achieving an optimized solution. In this paper, a modified technique based on a genetic algorithm (GA) to solve MOOPs, which are formulated by fuzzy relation constraints with - norm, is proposed. In this method, firstly, some techniques are utilized to reduce the size of the problem, so that the reduced problem can be solved easily. The proposed GA-based technique is then applied to solve the reduced problem locally. The most important advantage of this method is to solve a wide variety of MOOPs in the field of IoT, EC, and 5G. Furthermore, some numerical experiments are conducted to show the capability of the proposed technique. Not only does this method overcome the weaknesses of conventional methods owing to its potentials in the nonconvex feasible domain, but it also is useful to model complex systems.