Existence and uniqueness of the p-generalized modifierd error function

BOLLATI, JULIETA; SEMITIEL, JOSÉ A.; NATALE, MARÍA F.; TARZIA, DOMINGO A.

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS

Texas State University.

Año: 2020 vol. 2020 p. 1 - 11

1072-6691

In this article, we define a p-generalized modified error functionas the solution to a non-linear ordinary differential equation of second order,with a Robin type boundary condition at x = 0. We prove existence anduniqueness of a non-negative Cinfinity 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 aDirichlet boundary condition. In both problems, for p = 1, the generalizedmodified error function and the modified error function are recovered. Inaddition, we analyze the existence and uniqueness of solution to a problemwith a Neumann boundary condition.