Electronic Journal of Differential Equations, 
Vol. 2020 (2020), No. 35, pp. 1-11.

Title: Existence and uniqueness of the p-generalized modified error function

Authors: Julieta Bollati (CONICET, Argentina)
         Jose A. Semitiel (Univ. Austral, Rosario, Argentina)
         Maria F. Natale  (Univ. Austral, Rosario, Argentina)
         Domingo A. Tarzia (CONICET, Argentina)

Abstract:
 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
 $C^{\infty}$ solution by using a fixed point argument.
 We show 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
 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.
 
Submitted April 19, 2019. Published April 18, 2020.
Math Subject Classifications: 34A34, 47H10, 33E30, 34A12, 35R35.
Key Words: Modified error function; generalized modified error function;
           nonlinear ordinary differential equation; Banach fixed point theorem;
           Stefan problem.