info:eu-repo/semantics/article
Existence and uniqueness of the p-generalized modified error function
Fecha
2020-04Registro en:
Bollati, Julieta; Semitiel, José Abel; Natale, María Fernanda; Tarzia, Domingo Alberto; Existence and uniqueness of the p-generalized modified error function; Southwest Texas State University; University of North Texas; Electronic Journal of Differential Equations; 35; 4-2020; 1-11
1072-6691
1550-6150
CONICET Digital
CONICET
Autor
Bollati, Julieta
Semitiel, José Abel
Natale, María Fernanda
Tarzia, Domingo Alberto
Resumen
In this article, we define a p-generalized modified error function as the solution to a non-linear ordinary differential equation of second order, with a Robin type boundary condition at x = 0. We prove existence and uniqueness of a non-negative C∞ solution by using a fixed point argument. We show that the p-generalized modified error function converges to the pmodified error function defined as the solution to a similar problem with a Dirichlet boundary condition. In both problems, for p = 1, the generalized modified error function and the modified error function are recovered. In addition, we analyze the existence and uniqueness of solution to a problem with a Neumann boundary condition.