Existence and multiplicity results for double phase problem

By variational method, we obtain various existence and multiplicity results for the following double phase problem{−div(|∇u|p−2∇u+a(x)|∇u|q−2∇u)=f(x,u)in Ω,u=0on ∂Ω. In particular, we find a sign-changing ground state solution. Some properties of double phase operator are also obtained.