arXiv subjects

L. A. Maia

Publications and source records attributed to L. A. Maia.

3 recordsLinked to original sources

arXiv2021

Hartree-Fock type systems: existence of ground states and asymptotic behavior

In this paper we consider an Hartree-Fock type system made by two Schrödinger equations in presence of a Coulomb interacting term and a cooperative pure power and subcritical nonlinearity, driven by a suitable parameter $β\geq 0$. We show the existence of semitrivial and vectorial ground states solutions depending on the parameters involved. The asymptotic behavior with respect to the parameter $β$ of these solutions is also studied.

math.AP↗

arXiv2019

Mini-Max Algorithm via Pohozaev Manifold

A new algorithm for solving non-homogeneous asymptotically linear and superlinear problems is proposed. The ground state solution of the problem, which in general is obtained as a mini-max of the associated functional, is obtained as the minimum of the functional constrained to the Pohozaev manifold instead. Examples are given of the use of this method for finding numerical radially symmetric positive solutions depending on various parameters.

math.AP↗

arXiv2003

An alternative theoretical approach to describe planetary systems through a Schrodinger-type diffusion equation

In the present work we show that planetary mean distances can be calculated with the help of a Schrodinger-type diffusion equation. The obtained results are shown to agree with the observed orbits of all the planets and of the asteroid belt in the solar system, with only three empty states. Furthermore, the equation solutions predict a fundamental orbit at 0.05 AU from solar-type stars, a result confirmed by recent discoveries. In contrast to other similar approaches previously presented in the literature, we take into account the flatness of the solar system, by considering the flat solutions of the Schrodinger-type equation. The model has just one input parameter, given by the mean distance of Mercury.

astro-ph↗