Brake orbits type solutions to some class of semilinear elliptic equations期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

首页 | 本学科首页

官方微博 | 高级检索

Brake orbits type solutions to some class of semilinear elliptic equations

Authors:

Francesca Alessio Piero Montecchiari

Affiliation:

(1) Dipartimento di Scienze Matematiche, Università Politecnica delle Marche, Via Brecce Bianche, 60131 Ancona, Italy

Abstract:

We consider a class of semilinear elliptic equations of the form

$label{eq:abs} -Delta u(x,y)+a(x)W'(u(x,y))=0,quad (x,y)inmathbb{R}^{2}$

where

is a periodic, positive function and $${W:mathbb{R}tomathbb{R}}$$

is modeled on the classical two well Ginzburg-Landau potential ${W(s)=(s^{2}-1)^{2}}$ . We show, via variational methods, that if the set of solutions to the one dimensional heteroclinic problem

$$-ddot q(x)+a(x)W'(q(x))=0,quad xinmathbb{R},quad q(pminfty)=pm 1,$$

has a discrete structure, then (0.1) has infinitely many solutions periodic in the variable y and verifying the asymptotic conditions $${u(x,y)topm 1}$$

uniformly with respect to $${yinmathbb{R}}$$

. Supported by MURST Project ‘Metodi Variazionali ed Equazioni Differenziali Non Lineari’.

Keywords:

KeywordHeading" >Mathematics Subject Classification (2000) 35J60 35B05 35B40 35J20 34C37

本文献已被 SpringerLink 等数据库收录！

设为首页 | 免责声明 | 关于勤云 | 加入收藏