A Study of The Weighted (p,q)-Laplace Equation

Abstract

We prove the existence of solutions for the nonlinear partial differential equation -div(ω|∇v|^((p-2) ) ∇v)-div(ω|∇v|^((q-2) ) ∇v)= f_λ (v), v>0 in Ω v=0 on ∂Ω,

where, Ω⊆R^n is a smooth bounded domain, n≥3,λ>0,1<q<p<∞ and ω belongs to the Muckenhoupt class. When f_λ=λg(v)v^(-ρ), we use variational method to show the existence of a solution. When f_λ (v)=λv^(-ρ)+v^r, existence of atleast two solutions have been proved using the method of approximation.