Spectrum and bifurcation for semilinear elliptic problems in RN

被引：8

作者：

Dai, Guowei ^{[1
]}

Yao, Jinghua ^{[2
]}

Li, Fengquan ^{[1
]}

机构：

[1] Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China

[2] Indiana Univ, Dept Math, Bloomington, IN 47408 USA

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2017年 / 263卷 / 09期

关键词：

Bifurcation; Spectrum; Nodal solutions;

D O I：

10.1016/j.jde.2017.07.004

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper is concerned with the following semilinear elliptic problem {-Delta u = lambda m(x)f(u) in R-N, u -> 0 as vertical bar x vertical bar -> +infinity, where lambda is a real parameter and m is a weight function which may be sign-changing. For the linear case, i.e., f (u) = u, we investigate the spectral structure. For the semilinear case, we study the existence and asymptotic behavior of one-sign and nodal solutions by bifurcation method. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：5939 / 5967

页数：29

共 14 条

[1]

[Anonymous], HIROSHIMA MATH J

[2]

[Anonymous], 1980, Comm. Partial Differential Equations, DOI DOI 10.1080/03605308008820162

[3]

Constantin A, 1999, COMMUN PUR APPL MATH, V52, P949, DOI 10.1002/(SICI)1097-0312(199908)52:8<949::AID-CPA3>3.0.CO

[4]

2-D

[5] On the scattering problem for the Camassa-Holm equation [J].

Constantin, A .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2001, 457 (2008) :953-970

[6] STRUCTURE OF SOLUTIONS OF NONLINEAR EIGENVALUE PROBLEMS [J].

DANCER, EN .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1974, 23 (11) :1069-1076

[7] The Inverse Spectral Transform for the Conservative Camassa-Holm Flow with Decaying Initial Data [J].

Eckhardt, Jonathan .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2017, 224 (01) :21-52

[8] LINEAR AND SEMILINEAR EIGENVALUE PROBLEMS IN R(N) [J].

EDELSON, AL ;

RUMBOS, AJ .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1993, 18 (1-2) :215-240

[9] Global solution branches for semilinear equations in R(n) [J].

Edelson, AL ;

Furi, M .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1997, 28 (09) :1521-1532

[10]

GILBARG D., 2000, Elliptic Partial Differential Equations of Second Order, V2nd

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