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In this paper we prove the existence and the uniqueness of the weak solution of an orthotropic plate with stiffening ribs by methods of the abstract variational calculus. The solution of boundary value problem is obtained in the space $V(\Omega)\subset W_2^2(\Omega)$, where the bilinear form is $V(\Omega)$-elliptic. We introduce classical Galerkin's method for numerical solution Galerkin's approximation in space $V(\Omega)$ strongly converges to weak solution of boundary value problem in $V(\Omega)$.
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