Existence and uniqueness of the p-generalized modified error function

Julieta Bollati, María F. Natale, José A. Semitiel, Domingo A. Tarzia

Published 2018-10-09Version 1

In this paper, the p-generalized modified error function is defined as the solution to a non-linear ordinary differential problem of second order with a Robin type condition at $x=0$. Existence and uniqueness of a non-negative analytic solution is proved by using a fixed point strategy. It is shown that the p-generalized modified error function converges to the p-modified error function defined as the solution to a similar problem with a Dirichlet condition at x=0. In both problems, for p=1, the generalized modified error function and the modified error function, studied recently in literature, are recovered