Existence of three solutions for a nonlocal elliptic system of ( p , q ) Open image in new window-Kirchhoff type

In this paper, we study the solutions of a nonlocal elliptic system of ( p , q ) Open image in new window-Kirchhoff type on a bounded domain based on the three critical points theorem introduced by Ricceri. Firstly, we establish the existence of three weak solutions under appropriate hypotheses; then, we prove the existence of at least three weak solutions for the nonlocal elliptic system of ( p , q ) Open image in new window-Kirchhoff type.