Multiple small solutions for Kirchhoff equation with local sublinear nonlinearities. (September 2016)

• Record Type: Journal Article
• Authors: Wang, Li-Li; Han, Zhi-Qing
• Is Part Of: Applied mathematics letters. Volume 59(2016:Sep.)
• Page Start: 31
• Page End: 37
• Publication Date: 2016-09
• Subjects: Kirchhoff equation -- Symmetric mountain pass theorem -- Small solution -- Sublinear term; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2016.03.003
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: In this paper we discuss the following Kirchhoff equation in R N − ( a + b ∫ | ∇ u | 2 ) Δ u + V ( x ) u = f ( x, u ), where a, b > 0 are constants and N ≥ 3 . Without any growth condition for the nonlinear term f ( x, u ) on u at infinity, we obtain a sequence of solutions converging to zero in some Sobolev spaces.