On the critical p-Kirchhoff equation

2021/08/11 by Hasani, Erisa, Perera, Kanishka
#58E05 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary 35J92 #Secondary 35B33

paper · doi:10.48550/arxiv.2108.05285

Abstract

We study a nonlocal elliptic equation of p-Kirchhoff type involving the critical Sobolev exponent. First we give sufficient conditions for the (PS) condition to hold. Then we prove some existence and multiplicity results using tools from Morse theory, in particular, the notion of a cohomological local splitting and eigenvalues based on the Fadell-Rabinowitz cohomological index.

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