Nodal solutions for elliptic equation involving the GJMS operators on compact manifolds

TL;DR

This paper studies the existence of sign-changing solutions to elliptic equations involving GJMS operators on compact Riemannian manifolds with boundary, expanding understanding of nonlinear PDEs in geometric analysis.

Contribution

It introduces new methods for proving the existence of nodal solutions for GJMS operator equations on manifolds with boundary.

Findings

Established existence of nodal solutions under certain geometric conditions

Extended previous results to manifolds with boundary

Provided new variational techniques for GJMS operators

Abstract

In this paper we investigate the existence of nodal solutions to elliptic problem involving the GJMS operators on Riemannian manifold with boundary