Nodal solutions to quasilinear elliptic equations on compact Riemannian manifolds

TL;DR

This paper proves the existence of sign-changing solutions to certain nonlinear elliptic equations on compact Riemannian manifolds, and also establishes conditions under which such solutions do not exist.

Contribution

It introduces new existence results for nodal solutions to perturbed quasilinear elliptic equations with critical Sobolev exponent on compact manifolds.

Findings

Existence of nodal solutions under specific conditions

Nonexistence results for certain parameter ranges

Application of variational methods on Riemannian manifolds

Abstract

We show the existence of nodal solutions to perturbed quasilinear elliptic equations with critical Sobolev exponent on compact Riemannian manifolds. A nonexistence result is also given.