arXiv subjects

Pablo dos Santos Corrêa Junior

Publications and source records attributed to Pablo dos Santos Corrêa Junior.

2 recordsLinked to original sources

arXiv2026

Analysis of an Emden-Fowler-Hénon type equation

This work investigates a Hénon-type equation with the cap-shaped weight $V_α(|x|)=(4|x|(1-|x|))^α$, which concentrates on the sphere of radius $1/2$ as $α\to\infty$. Particular attention is devoted to ground state solutions and the phenomenon of symmetry breaking in the large-$α$ regime. A complete description of the asymptotic behavior of ground state radial solutions is obtained as $α\to\infty$. The analytical results are further supported by numerical simulations of the radial ground states.

math.AP↗

arXiv2024

Homoclinic Solution to Zero of a Non-autonomous, Nonlinear, Second Order Differential Equation with Quadratic Growth on the Derivative

This work aims to obtain a positive, smooth, even, and homoclinic to zero (i.e zero at infinity) solution to a non-autonomous, second-order, nonlinear differential equation involving quadratic growth on the derivative. We apply Galerkin's method combined with Strauss' approximation on the term involving the first derivative to obtain weak solutions. We also study the regularity of the solutions and the dependence on their existence with a parameter

math.CA↗