Analysis of Solutions for a Class of (p1(x), ..., pn(x))-Laplacian Systems with Hardy potentials

In this current work, we examine a (p1(x), ..., pn(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-Candito-D’Agu´ı [Adv. Nonlinear Stud. 14 (4), 915-939 (2014)] and a recent three critical points theorem of Bonanno-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 (p1(x), ..., pn(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.