Ricardo Roque Enguiça

Instituto Politécnico de Lisboa | ISEL · Departamento de Matemática

In this paper, we model mass running urban races, taking into consideration several conditioning factors. The main goal is to find ideal configurations of the start of the race, splitting it into several waves, reducing the density of athletes and the overall time lost, when comparing the normal race results with a race without density constraints....

We consider a time series with real data from a water lift station, equipped with three water pumps which are activated and deactivated depending on certain starting and halting thresholds. Given the water level and the number of active pumps, both read every 5 min, we aim to infer when each pump was activated or deactivated. To do so, we build an...

Hydropressor systems are of paramount importance in keeping water supplies running properly. A typical such device consists of two (or more) identical electropumps operating alternately, so as to avoid downtime as much as possible. A first challenge was, considering a dual pump configuration, to identify the ideal usage proportion of each pump (fro...

Injection moulding is a manufacturing process widely used in industry. A major step in this technique is the design of efficient cooling channels for the molten material. In this paper we develop a mathematical model for the automatic generation of conformal cooling channels which follow the shape of the mould. We focus on the core of the mould and...

In this paper we prove the existence of bounded solutions in the real line for the equation u¨+sign(u)=p(t)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ddot{u} + \m...

In this article we analyze some possibilities of finding positive solutions for second-order boundary-value problems with the Dirichlet and periodic boundary conditions, for which the corresponding Green's functions change sign. The obtained results can also be adapted to Neumann and mixed boundary conditions.

The authors investigate the following first-order differential equation y 0 = q(cy1/p − f(u)), where c is a positive parameter, p, q greater than unity, are conjugate numbers and f is a continuous function such that f(0) = f(1) = 0. Solutions satisfying y(0) = y(1) = 0 are of particular interest from the physical point of view. Indeed, the equation s...

In this paper we make an exhaustive study of the fourth order linear operator coupled with the clamped beam conditions u(0)=u(1)=u′(0)=u′(1)=0. We obtain the exact values on the real parameter M for which this operator satisfies an anti-maximum principle. Such a property is equivalent to the fact that the related Green’s function is nonnegative in...

We start by studying the existence of positive solutions for the differential equation u″=a(x)u−g(u), with u′(0)=u(+∞)=0, where a is a positive function, and g is a power or a bounded function. In other words, we are concerned with even positive homoclinics of the differential equation. The main motivation is to check that some well-known results c...

We study the existence of positive solutions for the differential equation

We extend a nonlocal maximum principle obtained in [2], which allows us to use a monotone method to find radial solutions of an elliptic problem in the presence of lower and upper solutions.

In this paper, we study the existence of solutions for the differential equation $$ u^{(4)}(t)=fig(t,u(t),u''(t)ig), $$ where $f$ satisfies one-sided Lipschitz conditions with respect to $u$ and $u''$, with periodic conditions or boundary conditions from ``simply supported'' beam theory. We assume the existence of lower and upper solutions (well-or...

We prove general existence results for x¢¢ = f(x)g(x¢), x(0) = x0, x¢(0) = x1,x^{\prime\prime} = f(x)g(x^{\prime}), x(0) = x_{0}, x^{\prime}(0) = x_{1}, where f and g need not be continuous or monotone. Moreover neither f nor g need be bounded around, respectively, x 0 and x 1, thus allowing singularities in the equation. Several other basic topic...

We consider the boundary value problem for the nonlinear Poisson equation with a nonlocal term −Δu=f(u,∫Ug(u)), u|∂U=0. We prove the existence of a positive radial solution when f grows linearly in u, using Krasnoselskiiés fixed point theorem together with eigenvalue theory. In presence of upper and lower solutions, we consider...

Concerning second order problems, we study the existence of positive solutions for the differential equation u = a(x)u − g (u) , with u (0) = u(+∞) = 0, where a is a positive function, g satisfies some growth hypotheses (in particular the bounded case). We also deal with the problem in which the differential equation has an extra dissipative term o...

We study the existence of positive solutions for the differential equation u ′′ (x) = a(x)u(x) − g (u (x)) , with u ′ (0) = u(+∞) = 0, where a is a positive function and g satisfies some growth hypotheses. The main motivation is to check that some well known results concerning the existence of homoclinics for the autonomous case (where a is constan...

In this paper, we study the existence of solutions for the differential equation u (4) (t) = f (t, u(t), u (t)) , where f satisfies one-sided Lipschitz conditions with respect to u and u , with pe-riodic conditions or the boundary conditions from "simply supported" beam theory. We assume the existence of lower and upper solutions (well-ordered and...