Multiple sign-changing solutions for Kirchhoff-type equations in R3: X. HE AND X. WU

In this paper, we study the following Kirchhoff-type equations -(a+b integral(R3) vertical bar del u vertical bar(2)dx) Delta u + V(x)u = vertical bar u vertical bar(p-2)u, x is an element of R-3, where a > 0, b >= 0, 4 < p < 2* = 6, and V is an element of C(R-3, 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, this problem has infinitely many sign-changing solutions. Copyright (c) 2017 John Wiley & Sons, Ltd