Existence and uniqueness of the p-generalized modified error function

BOLLATI, JULIETA; M.F. NATALE; J.A. SEMITIEL; DOMINGO A. TARZIA

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS

University of Texas

Lugar: Texas; Año: 2020 vol. 2020 p. 1 - 11

1072-6691

In this article, we dene a p-generalized modied error function as the solution to a non-linear ordinary dierential equation of second order, with a Robin type boundary condition at x = 0. We prove existence and uniqueness of a non-negative C1 solution by using a xed point argument.We show that the p-generalized modied error function converges to the p-modied error function dened as the solution to a similar problem with a Dirichlet boundary condition. In both problems, for p = 1, the generalized modied error function and the modied error function are recovered. In addition, we analyze the existence and uniqueness of solution to a problem with a Neumann boundary condition.