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arXiv · 1810.03934

Existence and uniqueness of the p-generalized modified error function

Julieta Bollati·María Fernanda Natale·José Abel Semitiel·Domingo Alberto Tarzia
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Abstract

In this paper, the p-generalized modified error function is defined as the solution to a non-linear ordinary differential problem of second order with a Robin type condition at x=0. Existence and uniqueness of a non-negative C^\infty solution is proved by using a fixed point strategy. It is shown 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 condition at x=0. In both problems, for p=1, the generalized modified error function and the modified error function, studied recently in literature, are recovered. In addition, existence and uniqueness of solution to a problem with a Neumann condition is also analysed.

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Julieta Bollati, María Fernanda Natale, José Abel Semitiel, Domingo Alberto Tarzia. 2018-10-09. Existence and uniqueness of the p-generalized modified error function. https://arxiv.org/abs/1810.03934

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