Abstract
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.
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