Existence and uniqueness of the p-generalized modified error function




Bollati, Julieta
Semitiel, Jose A.
Natale, Maria F.
Tarzia, Domingo A.

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Texas State University, Department of Mathematics


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 p-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.



Modified error function, Generalized modified error function, Nonlinear ordinary differential equation, Banach fixed point theorem, Stefan problem


Bollati, J., Semitiel, J. A., Natale, M. F., & Tarzia, D. A. (2020). Existence and uniqueness of the p-generalized modified error function. <i>Electronic Journal of Differential Equations, 2020</i>(35), pp. 1-11.


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