On the existence of ground state solutions to critical growth problems nonresonant at zero

TL;DR

This paper establishes the existence of ground state solutions for certain critical growth p-Laplacian and fractional p-Laplacian problems that are nonresonant at zero, expanding understanding of these nonlinear differential equations.

Contribution

It proves the existence of ground state solutions for critical growth p-Laplacian and fractional p-Laplacian problems that are nonresonant at zero, a novel result in this area.

Findings

Existence of ground state solutions for critical growth p-Laplacian problems.

Existence of ground state solutions for fractional p-Laplacian problems.

Solutions are nonresonant at zero.

Abstract

We prove the existence of ground state solutions to critical growth $p$-Laplacian and fractional $p$-Laplacian problems that are nonresonant at zero.