Juan Bosco Ferreiro

• PhD in Mathematics
• Professor at University of Santiago de Compostela

This is a Spanish into English translation of the paper by J. B. Ferreiro Darriba and Ó. López Pouso Límites utilizando coordenadas polares, La Gaceta de la RSME 7 (2004) no. 2, 405–434. It includes minor corrections to the original text.

The clothoid, also known as Cornu spiral or Euler spiral, is a curve widely used as a transition curve when designing the layout of railway tracks and roads because of a key feature: its curvature is proportional to its length. The classical method to compute a clothoid is based on the use of Taylor expansions of sine and cosine functions, usually...

This paper is devoted to the study of differential equations with piecewise constant arguments coupled with nonlinear boundary value conditions. Under suitable assumptions on the data of the equation, by means of the method of (weakly coupled) lower and upper solutions, we derive the existence of extremal solutions and extremal quasi-solutions. Mor...

This paper is devoted to the study of difference equations coupled with periodic boundary value conditions. We deduce the existence of at least one positive solution provided that the nonlinear part of the equation satisfies some monotonicity assumptions and the existence of a positive upper solution. The result is obtained from a new fixed point t...

This paper is devoted to the existence of solutions for a problem of first order difference equations with maxima and with nonlinear functional boundary value conditions. Such boundary conditions include, among others, initial, periodic, antiperiodic and multipoint boundary value conditions, as particular cases.

Se demuestran varios resultados en relación con el límite cuando (x, y) tiende a (a, b) de una función real de dos variables reales f(x, y). Se presta especial atención al uso de las coordenadas polares para calcular dicho límite. Los resultados se acompañan con ejemplos. English translation: We prove several results concerning the limit as (x, y)...

In this paper we obtain the expression of the Green's function related with a first order periodic differential equation with piecewise constant argument. We derive comparison results for the treated linear operator by studying the sign of the obtained Green's function.

In this paper we derive new discrete Halanay-type inequalities and show some applications in the investigation of the asymptotic behavior of nonlinear difference equations. In particular, difference equations involving the “maximum” functional are considered.

In this note, we prove a discrete analogue of the continuous Halanay inequality and apply it to derive sufficient conditions for the global asymptotic stability of the equilibrium of certain generalized difference equations. The relation with some numerical schemes for functional delay differential equations is discussed.

In this paper we establish comparison results (maximum principles) which allow us to use the monotone method and the method of upper and lower solutions in order to build convergent sequences to the solutions of differ-ence equations of