Positive and negative solutions for a class of Kirchhoff type problems on unbounded domain. (February 2015)

• Record Type: Journal Article
• Authors: Fan, Haining; Liu, Xiaochun
• Is Part Of: Nonlinear analysis. Volume 114(2015)
• Page Start: 186
• Page End: 196
• Publication Date: 2015-02
• Subjects: 35A15 -- 35B33 -- 35J62; Multiple solutions -- Nonlocal problems -- Variational method; 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.2014.07.012
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we study the existence of multiple positive and negative solutions for a class of Kirchhoff type problems on an unbounded domain. Using the variational methods, we show that our problem admits at least two positive and two negative solutions under different conditions. A cut-off functional is utilized to obtain the bounded Palais–Smale sequences.