Electronic Journal of Differential Equations, Vol. 2025 (2025), No. 19, pp. 1-29.

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

Authors: Eduardo H. Caqui (INFES-UFF, Santo Antonio de Padua, Brazil)
         Sandra M. de S. Lima (INFES-UFF, Santo Antonio de Padua, Brazil)
         Fabio R. Pereira (Univ. Federal de Juiz de Fora, MG, Brazil)
  
Abstract:
We study the existence of solutions for 
Ambrosetti-Prodi type systems involving the fractional Laplace
operator, and having 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 studied.


Submitted April 6, 2024. Published February 26, 2025.
Math Subject Classifications: 35B06, 35B09, 35J15, 35J20.
Key Words: Ambrosetti-Prodi problem; fractional systems; resonance; critical growth.