(Pontificia Universidad Católica del Perú, 2023-12-29) Ipanaque Zapata, Cesar A.
A classic problem in analysis is to solve nonlinear equations of the form F (x) = 0, where F : Dn → Rm is a continuous map of the closed unit disk Dn ⊂ Rn in Rm. A topological technique, which exists in the literature, for the existence of solutions of nonlinear equations is the topological degree theory. In this work, we will use the category of a map theory to solve the problem of existence of solutions of nonlinear equations. This theory, as we will show in this work, provides an alternative topological technique to study nonlinear equations.
(Pontificia Universidad Católica del Perú, 2023-12-29) Falla Luza, Maycol
We give examples of germs of surfaces containing a rational curve with positive self-intersection and with zero, one or two independent meromorphic functions.
(Pontificia Universidad Católica del Perú, 2023-12-29) Casavilca, Juan E.
This article introduces a new concept of solution of a linear singular system (descriptor system), based on minimization. It is shown that, by imposing a hypothesis on the matrices of the descriptor system, the minimization-based solution exists and is unique for any initial condition. In particular, if the initial condition is consistent, then the minimization-based solution is equal to the classical solution. Also in this work, a numerical example is given in order to analyze the minimization-based solutions for different initial conditions.
