An elliptic equation under the effect of two nonlocal terms

The aim of this note is to investigate the existence of signed and sign‐changing solutions to the Kirchhoff type problem (0.1) where Ω is a bounded smooth domain in (N = 1,2,3), a,b > 0 and 2 < p < 2^?, with 2^?=+∞ if N = 1,2 and 2^?=6 if N = 3. Using variational methods, we show that (0.1) possesses three solutions of mountain pass type (one positive, one negative and one sign‐changing) and infinitely many high‐energy sign‐changing solutions. Copyright © 2015 John Wiley & Sons, Ltd.