Abstract. We consider a model of a long Josephson junction where the thickness of the dielectric layer represents a lattice of resistive inhomogeneities. In the original formulation of this model the inhomogeneities were modeled by Dirac's 8-functions [1-4]. In this paper we study a junction with a finite size of inhomogeneities. Mathematically, the model reduces to the stationary inhomogeneous sine-Gordon equation — ϕ_xx + j_D(x)sinϕ + γ = 0, with given periodic function j_D(x) and periodic boundary conditions. We demonstrate numerically, the existence of stable stationary states with spatial period greater than a certain value. Our numerical calculations are based on the continuous analog of the Newton's method.

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