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 Hardypotentials. We establish the existence of at least one non-zero critical point and atleast three distinct critical points to this system from an abstract critical point resultof Bonanno et al. (Adv Nonlinear Stud 14(4):915-939, 2014) and a recent three criti-cal 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(p1(x),...,pn(x))-Laplacian systems with Hardy potentials, in which the nonlinear-ity in Omega may change sign. Furthermore, we provide an example to illustrate our mainconclusions.