Multiple positive and sign-changing solutions for a class of Kirchhoff equations.

This paper is concerned with the existence of multiple non-radial positive and sign-changing solutions for the following Kirchhoff equation: − a + b ∫ ℝ 3 | ∇ u | 2 Δ u + (1 + λ Q (x)) u = | u | p − 2 u , in ℝ 3 , (0. 1) where a , b > 0 are constants, p ∈ (2 , 6) , λ is a parameter, and Q (x) is a potential function. Under the assumption on Q (x) with exponential decay at infinity, we construct multi-peak positive and sign-changing solutions for problem (0.1) as λ → ∞ (or 0), where the peaks concentrate at infinity. [ABSTRACT FROM AUTHOR]