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We investigate the following elliptic equations:⎧⎩⎨−M(∫R Nϕ(|∇u|2)dx)div(ϕ′(|∇u|2)∇u)+|u|α−2 u=λh(x,u),u(x)→0,as|x|→∞,in R N,where N≥2,1<p<q<N,α<q,1<α≤p∗q′/p′with p∗=NpN−p,ϕ(t)behaves like t q/2 for small t and t p/2 for large t,and p′and q