We prove the existence of solutions for the following boundary value problem −𝑑𝑖𝑣(𝜔|∇𝑣|𝑝−2∇𝑣)−𝑑𝑖𝑣(𝜔|∇𝑣|𝑞−2∇𝑣)=𝑓𝜆(𝑣),𝑣>0 𝑖𝑛 Ω 𝑣=0 𝑜𝑛 𝜕Ω, where Ω⊆ℝ𝑛 is a smooth bounded domain, 𝑛≥3,𝜆>0,1<𝑞<𝑝<∞ and 𝜔 𝜖𝐴𝑝. For suitable values of 𝜌 and 𝑟, when 𝑓𝜆(𝑣)=𝜆𝑔(𝑣)𝑣−𝜌, we use the variational method to show the existence of a solution and when 𝑓𝜆(𝑣)= 𝜆𝑣−𝜌+𝑣𝑟, the existence of at least two solutions have been proved using the method of approximation.