Unilateral Global Bifurcation for Eigenvalue Problems with Homogeneous Operator

被引：1

作者：

Dai, Guowei ^{[1
]}

Feng, Zhaosheng ^{[2
]}

机构：

[1] Dalian Univ Technol, Sch Math Sci, Dalian 11602, Liaoning, Peoples R China

[2] Univ Texas Rio Grande Valley, Sch Math & Stat Sci, Edinburg, TX 78539 USA

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2019年 / 29卷 / 06期

关键词：

Global bifurcation; homogeneous operator; Monge-Ampere equation; one-sign solution; P-LAPLACIAN; ELLIPTIC-EQUATIONS; DIRICHLET PROBLEM; 1ST EIGENVALUE; REGULARITY; REAL;

D O I：

10.1142/S0218127419500846

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We focus on the structure of the solution set for the nonlinear equation u = L (lambda)u + H(lambda, u), where L(.) and H(lambda, u) are continuous operators. Under certain hypotheses on L(.) and H(., .), unilateral global bifurcations for eigenvalue problems are presented. Some applications are illustrated for nonlinear ordinary and partial differential equations. In particular, the existence and multiplicity of one-sign solutions for Monge-Ampere equation is discussed.

引用

页数：15