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

2024/06/03 by Pablo dos Santos Corrêa Junior, Junior, Pablo dos Santos Corrêa, Luiz F. O. Faria +1
Mathematics · Computer Science · #Differential Equations and Numerical Methods #Advanced Mathematical Modeling in Engineering #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.2406.01772

Abstract

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

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