In this article, the solvability of the second boundary value problem for the fully nonlinear Gilbarg–Serrin equation, which belongs to the class of second-order elliptic equations with discontinuous coefficients, is investigated in the weighted Sobolev space Wγ2,p(Ω), by incorporating the corresponding weight w(x) = rγ. Under the imposed conditions, when the function µ(r) takes large values, i.e., when limr→0 µ(r) = +∞, the qualitative characteristics of the fully nonlinear Gilbarg–Serrin equation differ significantly from those of harmonic functions [1;3], and the uniqueness of the solution to the second boundary value problem is ensured in the unweighted Sobolev space W 2,p(Ω) [4;5;6]. The main goal of the article is to demonstrate the weak uniqueness and solvability of the second boundary value problem in the weighted Sobolev spaces Wγ2,p(Ω) and Wγ2,p(Ω). This is achieved by proving certain inequalities satisfied by the function u(x) when x ∈ Ω, and by establishing the corresponding theorems.