Multiplicity results for critical fractional Ambrosetti-Prodi type system with 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.

33 pages. F. R. Pereira was supported partially by FAPEMIG/Brazil (RED-00133-21) and FAPEMIG/Brazil (CEX APQ 04528/22)