# Existence and uniqueness of the p-generalized modified error function

 dc.contributor.author Bollati, Julieta dc.contributor.author Semitiel, Jose A. dc.contributor.author Natale, Maria F. dc.contributor.author Tarzia, Domingo A. dc.date.accessioned 2021-09-22T17:47:29Z dc.date.available 2021-09-22T17:47:29Z dc.date.issued 2020-04-18 dc.description.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∞ 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. dc.description.department Mathematics dc.format Text dc.format.extent 11 pages dc.format.medium 1 file (.pdf) dc.identifier.citation Bollati, J., Semitiel, J. A., Natale, M. F., & Tarzia, D. A. (2020). Existence and uniqueness of the p-generalized modified error function. Electronic Journal of Differential Equations, 2020(35), pp. 1-11. dc.identifier.issn 1072-6691 dc.identifier.uri https://hdl.handle.net/10877/14539 dc.language.iso en dc.publisher Texas State University, Department of Mathematics dc.rights Attribution 4.0 International dc.rights.uri https://creativecommons.org/licenses/by/4.0/ dc.source Electronic Journal of Differential Equations, 2020, San Marcos, Texas: Texas State University and University of North Texas. dc.subject Modified error function dc.subject Generalized modified error function dc.subject Nonlinear ordinary differential equation dc.subject Banach fixed point theorem dc.subject Stefan problem dc.title Existence and uniqueness of the p-generalized modified error function dc.type Article

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