Analysis of solutions for a class of (p1(x),…,pn(x))-Laplacian systems with Hardy potentials

In this current work, we examine a ( p 1 ( x ) , … , p n ( x ) ) -Laplacian system with Hardy potentials. We establish the existence of at least one non-zero critical point and at least three distinct critical points to this system from an abstract critical point result of Bonanno et al. (Adv Nonlinear Stud 14(4):915–939, 2014) and a recent three critical points theorem of Bonanno and Marano (Appl Anal 89:1–10, 2010). This article represents, as far as we are aware, one of the first efforts towards the study of the ( p 1 ( x ) , … , p n ( x ) ) -Laplacian systems with Hardy potentials, in which the nonlinearity in Ω may change sign. Furthermore, we provide an example to illustrate our main conclusions.