Infinitely many solutions for a Kirchhoff problem with a subcritical exponent

作者：Chen, Mengyao; Li, Qi^*

来源：Journal of Mathematical Analysis and Applications, 2022, 507(2): 125772.

DOI：10.1016/j.jmaa.2021.125772

• Kirchhoff problem
• Lyapunov-Schmidt reduction
• Subcritical exponent

This article deals with the following Kirchhoff problem: @@@ - (a + b integral(RN )vertical bar del u vertical bar(2)) Delta u + u = K(x)vertical bar u vertical bar(p-1)u in R-N, (0.1) @@@ where a, b > 0, 1 < p < 2* - 1, 2* = , 2N/n - 2, and K(x) is a potential function. We prove that problem (0.1) has infinitely many solutions by using Lyapunov-Schmidt reduction. Our results extend and improve the results for the Schriidinger equation obtained by Badiale (2002) [3].