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: [Formula: see text] where [Formula: see text] are constants, [Formula: see text], [Formula: see text] is a parameter, and [Formula: see text] is a potential function. Under the assumption on [Formula: see text] with exponential decay at infinity, we construct multi-peak positive and sign-changing solutions for problem (0.1) as [Formula: see text] (or [Formula: see text]), where the peaks concentrate at infinity.