Multiple solutions in fractional Orlicz-Sobolev Spaces for a class of nonlocal Kirchhoff systems

Abstract

The existence and multiplicity of solutions for a class of nonlocal elliptic systems are investigated in this paper. We show that there are precise intervals of positives parameters that the energy function associated with the Kirchhoff system problem admits three critical points which are exactly the weak solutions to our problem and another interval of positives parameters that admit many solutions to the Kirchhoff system problem without the boundedness condition of the Kirchhoff function. Our strategy is focused on the use of variational approaches.