Existence and nonexistence results of polyharmonic boundary value problems with supercritical growth

TL;DR

This paper investigates conditions for the existence and nonexistence of solutions to polyharmonic boundary value problems with supercritical growth, using truncation, $L^{ obreak ext{infinity}}$ bounds, and variational identities.

Contribution

It introduces new existence and nonexistence results for polyharmonic problems with supercritical growth, employing novel analytical techniques.

Findings

Established existence results using truncation and $L^{ obreak ext{infinity}}$ bounds.

Derived nonexistence results via Pucci-Serrin's variational identity.

Provides conditions under which solutions do or do not exist for these boundary value problems.

Abstract

We establish some existence results of polyharmonic boundary value problems with supercritical growth. Our approach is based on truncation argument as well as $L^{\infty}$-bounds. Also, by virtue of Pucci-serrin's variational identity \cite{PS}, we provide some nonexistence results.