Multiplicity of weak solutions to Steklov problem involving weighted p(.)-Laplacian-like operator

We study a nonlinear Steklov problem involving weighted p(.)-Laplacian-like operator. Using some variational methods, we obtain the existence and multiplicity of solutions for the following problem $${aligned} \{ {array}{cc} div( ( 1+{| ∇ u| ᵖ⁽ˣ⁾}{ √{1+| ∇ u| ²ᵖ⁽ˣ⁾}}) a(x)| ∇ u| ᵖ⁽ˣ⁾⁻²∇ u) =b(x)| u| ᵖ⁽ˣ⁾⁻²u, & in Ω \\ ( 1+{| ∇ u| ᵖ⁽ˣ⁾}{√{1+| ∇ u| ²ᵖ⁽ˣ⁾}}) a(x)| ∇ u| ᵖ⁽ˣ⁾⁻²∂ u/∂ υ =λ f(x,u), & on ∂ Ω ,{array} . {aligned}$$ under some suitable conditions.