Nodal solutions for fourth order elliptic equations with critical exponent on compact manifolds

TL;DR

This paper proves the existence of nodal solutions for fourth-order elliptic equations with critical Sobolev growth on compact Riemannian manifolds using variational methods.

Contribution

It introduces a variational approach to establish nodal solutions for boundary value problems involving critical exponent fourth-order elliptic equations.

Findings

Existence of nodal solutions on compact manifolds

Application of variational methods to critical growth problems

Extension to manifolds with boundary

Abstract

Using a variational method we prove the existence of nodal solutions to prescribed scalar Q- curvature type equations on compact Riemannian manifolds with boundary; these equations are fourth-order elliptic equations with critical Sobolev growth .