Heteroclinic solutions for some classes of prescribed mean curvature equations in whole ℝ²

2024/04/17 by Claudianor O. Alves, Alves, Claudianor O., Renan J. S. Isneri +1
Mathematics · #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2404.11689

openalex publication_date 2024/04/17 · openalex created_date 2024/04/20 · openalex updated_date 2026/07/28

Abstract

The purpose of this paper consists in using variational methods to establish the existence of heteroclinic solutions for some classes of prescribed mean curvature equations of the type -div((∇ u)/(√(1+|∇ u|²))) + A(εx,y)V'(u)=0~~ in ~~ℝ², where ε>0 and V is a double-well potential with minima at t=α and t=β with α<β. Here, we consider some class of functions A(x,y) that are oscillatory in the variable y and satisfy different geometric conditions such as periodicity in all variables or asymptotically periodic at infinity.

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