Multiple Sign-Changing Solutions for Kirchhoff-Type Equations. (13th December 2015)

• Record Type: Journal Article
• Authors: Li, Xingping; He, Xiumei
• Other Names: Bonanno Gabriele Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2015(2015)
• Publication Date: 2015-12-13
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2015/985986
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : We study the following Kirchhoff-type equations- a + b ∫ Ω ∇ u 2 d x Δ u + V x u = f x, u, inΩ, u = 0, in∂ Ω, whereΩ is a bounded smooth domain ofR N ( N = 1, 2, 3 ), a > 0, b ≥ 0, f ∈ C ( Ω ¯ × R, R ), andV ∈ C ( Ω ¯, R ) . Under some suitable conditions, we prove that the equation has three solutions of mountain pass type: one positive, one negative, and sign-changing. Furthermore, iff is odd with respect to its second variable, this problem has infinitely many sign-changing solutions.