Multiple Sign-Changing Solutions for Kirchhoff-Type Equations. (13th December 2015) - Li, Xingping; He, Xiumei
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.