On a class of anisotropic elliptic equations without Ambrosetti–Rabinowitz type conditions

This article investigates a class of anisotropic elliptic equations with non-standard growth conditions {−∑i=1N∂xi(|∂xiu|pi(x)−2∂xiu)=f(x,u)in  Ω,u=0on  ∂Ω, where Ω⊂RNΩ⊂RN (N≥3N≥3) is a bounded domain with smooth boundary ∂Ω∂Ω, and pipi, i=1,2,…,Ni=1,2,…,N are continuous functions on Ω¯ such that 1