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By using the well-known Leggett–Williams multiple fixed point theorem for cones, some new criteria are established for the existence of three positive periodic solutions for a class of n-dimensional functional differential equations with impulses of the form ( y′(t) = A(t)y(t) + g(t, yt), t 6= tj , j ∈ Z, y(t+j ) = y(t − j ) + Ij(y(tj)), where A(t) = (aij(t))n×n is a nonsingular matrix with continuous real-valued entries.

Three periodic solutions for a class of higher-dimensional functional differential equations with impulses