Multiplicity of solutions of weighted (p,q)-Laplacian with small source

In this article, we study the existence of infinitely many solutions to the degenerate quasilinear elliptic system -div(h1(x)|∇u|p-2∇u)=d(x)|u|r-2u+Gu(x,u,υ)-div(h2(x)|∇υ|q-2∇υ)=f(x)|υ|s-2υ+Gυ(x,u,υ)u=υ=0inΩinΩon∂Ωwhere Ω is a bounded domain in RN with smooth boundary ∂Ω, N≥2, 1 < r < p < ∞, 1 < s < q < ∞; h1(x) and h2(x) are allowed to have “essential” zeroes at some points in Ω;d(x)|u|r-2u and f(x)|υ|s-2υ are small sources with Gu(x,u,v), Gv(x,u,v) being their high-order perturbations with respect to (u,v) near the origin, respectively.