On positive solutions of biharmonic elliptic inequalities on Riemannian manifolds

TL;DR

This paper studies when positive solutions exist or do not exist for biharmonic elliptic inequalities on Riemannian manifolds, identifying critical exponents based on geometric conditions.

Contribution

It introduces new criteria involving Green functions and volume growth to determine the existence of positive solutions for biharmonic inequalities on manifolds.

Findings

Established the critical exponent for biharmonic inequalities.

Derived conditions for non-existence of positive solutions.

Linked geometric properties of manifolds to solution behavior.

Abstract

We investigate the non-existence and existence of positive solutions to biharmonic elliptic inequalities on manifolds. Using Green function and volume growth conditions, we establish the critical exponent for biharmonic problem.