Variational methods for degenerate Kirchhoff equations

TL;DR

This paper develops variational methods to find solutions for degenerate Kirchhoff equations with nonlinearities of Berestycki-Lions type, addressing different spatial dimensions with tailored approaches.

Contribution

It introduces novel variational techniques for degenerate Kirchhoff equations across various dimensions, employing mountain pass and Clark theorem methods.

Findings

Existence of solutions for N=2,3 using mountain pass methods.

Existence of solutions for N≥5 using Clark theorem.

Extension of variational methods to degenerate Kirchhoff problems.

Abstract

For a degenerate autonomous Kirchhoff equation which is set on $\mathbb{R}^N$ and involves the Berestycki-Lions type nonlinearity, we cope with the cases $N=2,3$ and $N\geq5$ by using mountain pass and symmetric mountain pass approaches and by using Clark theorem respectively.