Bifurcation results for a Kirchhoff type problem involving sign-changing weight functions. (June 2020)

• Record Type: Journal Article
• Authors: Xu, Xian; Qin, Baoxia; Chen, Siyu
• Is Part Of: Nonlinear analysis. Volume 195(2020)
• Publication Date: 2020-06
• Subjects: 35J25 -- 35J61 -- 35B32 -- 35P30; Bifurcation -- Nonlocal elliptic -- Kirchhoff type; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.111718
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we establish some existence results for both compact and unbounded connected components of the positive solutions set of a nonlocal problem of the Kirchhoff type. The methods to show our main results are the local and global bifurcation techniques, a priori bounds for elliptic equation, and the properties of the principal eigenvalues. To obtain the a priori bounds for Kirchhoff type elliptic equation, some new techniques are introduced.