Quasilinear elliptic problem without Ambrosetti-Rabinowitz condition involving a potential in Musielak-Sobolev spaces setting

Soufiane Maatouk, Abderrahmane El Hachimi

In this paper, we consider the following quasilinear elliptic problem with potential $$(P) \begin{cases} -\mbox{div}(ϕ(x,|\nabla u|)\nabla u)+ V(x)|u|^{q(x)-2}u= f(x,u) & \ \ \mbox…