New Trends in Differential and Difference Equations and Applications

This is a reprint of articles from the Special Issue published online in the open-access journal Axioms (ISSN 2075-1680) from 2018 to 2019 (available at https://www.mdpi.com/journal/axioms/special issues/differential difference equations)

Boundary value problems for hybrid differential equations

This note is motived from some papers treating  the hybrid differential equations. An existence theorem for this equation is proved. Some fundamental differential inequalities for hybrid differential equatins  are also established which are utilized to prove the existence of extremal solutions. Necessary tools are considered and the comparison principle is proved which will be useful for further study of qualitative behavior of solutions

Stability analysis of partial differential variational inequalities in Banach spaces

In this paper, we study a class of partial differential variational inequalities. A general stability result for the partial differential variational inequality is provided in the case the perturbed parameters are involved in both the nonlinear mapping and the set of constraints. The main tools are theory of semigroups, theory of monotone operators, and variational inequality techniques

Order Management System Proposal Using Inventory Balance Equation with Non-continuous Replenishment

The purpose of this paper is to present an inventory balance model including an order-up-to replenishment policy with partial backlogging. Pictured in the model is a situation, where goods are not replenished continuously, but only at predetermined intervals. The model is described by ordinary differential equations with delayed argument because of the assumption of a time lag between ordering and delivery. A computer simulation which helps to demonstrate and verify model behaviour is utilized for the numerical solution of the model. Sales data of a real company are used as the input data. Due to the comparison of the designed model outputs against the real state in the company, it was verified that it is possible to achieve a substantial reduction in warehousing costs without a disproportionate increase in the risk of inventory shortage. The authors note that modern methods of functional analysis can be successfully applied in solving an inventory balance model

Una aproximación a los conjuntos alcanzables de una inclusión diferencial difusa

Se estudian los sistemas dinámicos difusos a partir de la noción de inclusión diferencial difusa introducida en [24]. Se analizan algunas técnicas utilizadas para resolver inclusiones diferenciales difusas asociadas a problemas de valor inicial, y se introduce una nueva forma de aproximación a los conjuntos alcanzables difusos, la cual permite resolver de manera más natural una inclusión diferencial difusa.From the notion of fuzzy differential inclusion introduced in [24],fuzzy dynamical systems are studied. Some techniques used to solve fuzzy differential inclusions associated to initial value problems are discussed. Anew approximation technique for fuzzy attainable sets which allows to solve in a more natural way a fuzzy differential inclusion is introduced

Existencia de solución de un sistema hiperbólico no lineal con condición de inclusión en la frontera

Estudia un sistema hiperbólico no lineal con un término discontinuo multivaluado y con término de amortiguamiento no lineal de segundo orden sobre la frontera, respecto a la existencia de solución generalizada y el comportamiento asintótico exponencial de su energía asociada al sistema dado por una ecuación específica. Se ha trabajado con la técnica dada por una consecuencia del Lema de Nakao, aplicada a energías definidas sobre subespacios finitamente generado, para luego, pasando al límite, obtener el decaimiento tanto, exponencial como polinomial. Se han tenido muchos cuidados con las estimativas de la energía tanto a derecha como a izquierda. Estas aproximaciones por energía definidas en subespacios finitamente generado pueden ser aplicables a otros problemas de E.D.P. Los problemas con inclusión diferencial generalmente se presentan en la teoría de decisiones y en la física, en especial en mecánica de sólidos.Tesi

Set-Valued Analysis

This Special Issue contains eight original papers with a high impact in various domains of set-valued analysis. Set-valued analysis has made remarkable progress in the last 70 years, enriching itself continuously with new concepts, important results, and special applications. Different problems arising in the theory of control, economics, game theory, decision making, nonlinear programming, biomathematics, and statistics have strengthened the theoretical base and the specific techniques of set-valued analysis. The consistency of its theoretical approach and the multitude of its applications have transformed set-valued analysis into a reference field of modern mathematics, which attracts an impressive number of researchers