Nodal solutions of fourth-order Kirchhoff equations with critical growth in $\mathbb{R}^N$

TL;DR

This paper investigates the existence of sign-changing solutions for a class of fourth-order Kirchhoff equations with critical growth in Euclidean space, using variational methods on the Nehari manifold.

Contribution

It introduces a new approach to establish the existence of nodal solutions for Kirchhoff-type equations with critical growth in unbounded domains.

Findings

Existence of nodal solutions under certain conditions.

Application of constrained minimization on the Nehari manifold.

Extension of methods to critical growth problems.

Abstract

We consider a class of fourth-order elliptic equations of Kirchhoff type with critical growth in $\mathbb{R}^N$. By using constrained minimization in the Nehari manifold, we establish sufficient conditions for the existence of nodal (that is, sign-changing) solutions.