Multiplicity results for critical fractional Ambrosetti-Prodi type system with nonlinearities interacting with the spectrum

TL;DR

This paper studies the existence of solutions for fractional Ambrosetti-Prodi systems with critical nonlinearities, including resonant cases, expanding understanding of such systems in spectral and fractional Laplacian contexts.

Contribution

It introduces new existence results for fractional Ambrosetti-Prodi systems with critical growth nonlinearities, including analysis at spectral resonance points.

Findings

Existence of solutions established for non-resonant cases.

Results extended to resonant spectral cases.

Analysis of nonlinearities interacting with the spectrum.

Abstract

We investigated the existence of solutions for a class of Ambrosetti-Prodi type systems involving the fractional Laplacian operator and with nonlinearities reaching critical growth and interacting, in some sense, with the spectrum of the operator. The resonant case in $\lambda_{k,s}$ for $k>1$ is also investigated.