Some new entire solutions of semilinear elliptic equations on Rn

被引：36
作者：
Malchiodi, Andrea [1 ]
机构：
[1] SISSA, Sector Funct Anal, I-34014 Trieste, TS, Italy
来源：
ADVANCES IN MATHEMATICS | 2009年 / 221卷 / 06期
关键词：
Semilinear elliptic equations; Entire solutions; Lyapunov-Schmidt reduction; Weighted spaces; NONLINEAR SCHRODINGER-EQUATIONS; PERTURBED NEUMANN PROBLEM; CONSTANT MEAN-CURVATURE; CONCENTRATION-COMPACTNESS PRINCIPLE; INTERIOR PEAK SOLUTIONS; LEAST-ENERGY SOLUTIONS; POSITIVE SOLUTIONS; UNBOUNDED-DOMAINS; LAYER SOLUTIONS; BOUND-STATES;
D O I：
10.1016/j.aim.2009.03.012
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove existence of a new type of positive solutions of the semilinear equation -Delta u + u = u(p) on R-n, where 1 < p < n+2/n-2. These solutions are bounded, but do not tend to zero at infinity. Indeed, they decay to zero away from three half-lines with a common origin, and their asymptotic profile is periodic along these half-lines. (C) 2009 Elsevier Inc. All rights reserved.
引用
收藏
页码：1843 / 1909
页数：67
相关论文
共 61 条
[1]   Singularly perturbed elliptic equations with symmetry: Existence of solutions concentrating on spheres, part II [J].
Ambrosetti, A ;
Malchiodi, A ;
Ni, WM .
INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2004, 53 (02) :297-329
[2]   Singularly perturbed elliptic equations with symmetry: Existence of solutions concentrating on spheres, part I [J].
Ambrosetti, A ;
Malchiodi, A ;
Ni, WM .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2003, 235 (03) :427-466
[3]   Semiclassical states of nonlinear Schrodinger equations [J].
Ambrosetti, A ;
Badiale, M ;
Cingolani, S .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1997, 140 (03) :285-300
[4]   Multiplicity results for some nonlinear Schrodinger equations with potentials [J].
Ambrosetti, A ;
Malchiodi, A ;
Secchi, S .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2001, 159 (03) :253-271
[5]  
Ambrosetti A., 2005, PROGR MATH, V240
[6]   Concentration around a sphere for a singularly perturbed Schrodinger equation [J].
Badiale, M ;
D'Aprile, T .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2002, 49 (07) :947-985
[7]   On the existence of a positive solution of semilinear elliptic equations in unbounded domains [J].
Bahri, A ;
Lions, PL .
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1997, 14 (03) :365-413
[8]  
Bahri A., 1990, REV MAT IBEROAM, V6, P1, DOI DOI 10.4171/RMI/92
[9]   The semiclassical limit of the nonlinear Schrodinger equation in a radial potential [J].
Benci, V ;
D'Aprile, T .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2002, 184 (01) :109-138
[10]  
BERESTYCKI H, 1983, ARCH RATION MECH AN, V82, P313
1234567