Multiplicity of solutions to a nonlinear elliptic problem on a Riemannian orbifold

TL;DR

This paper uses the photography method to establish a lower bound on the number of solutions for a nonlinear elliptic problem on a Riemannian orbifold, linking it to the orbifold's topological complexity.

Contribution

It introduces a novel application of the photography method to relate solution multiplicity to the Lusternik--Schnirelmann category of orbifold submanifolds.

Findings

Lower bound for solutions based on orbifold topology

Connection between solution count and local group structure

Method applicable to nonlinear elliptic problems on orbifolds

Abstract

We employ the photography method to obtain a lower bound for the number of solutions to a nonlinear elliptic problem on a Riemannian orbifold in function of the Lusternik--Schnirelmann category of its submanifold of points with largest local group.