Slope-changing solutions of elliptic problems on Rn

被引：16

作者：

Bessi, Ugo ^{[1
]}

机构：

[1] Univ Roma Tre, Dipartimento Matemat, I-00146 Rome, Italy

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2008年 / 68卷 / 12期

关键词：

D O I：

10.1016/j.na.2007.04.031

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the problem -Delta u + Fu(x, u) = 0 on R-n, where F is a smooth function periodic of period I in all its variables. We are going to find a non-degeneracy condition on F for which the following holds. If we are given a sequence of positive integers {(N) over tilde (i)}(i epsilon Z) and a sequence {alpha(i)}(i epsilon Z) of real numbers (the slopes), then we shall find an increasing sequence {Q(i)} of integers and a solution u which is entire, periodic in (x(2), . . . , x(n)) and which is close to the plane alpha(1)(x(1) - Q(i)) + u(Q(i), 0, . . . , 0) for x(1) epsilon [Q(i), Q(i) + (N) over tilde (i)]. (C) 2007 Elsevier Ltd. All rights reserved.

引用

页码：3923 / 3947

页数：25

共 16 条

[1] On a long-standing conjecture of E.!De Giorgi:: Symmetry in 3D for general nonlinearities and a local minimality property [J].