Convolution complementarity problems have the form 0 ≤ u(t) ⊥ (k∗u)(t)+q(t) ≥ 0 for all t. These are shown to have solutions provided k(t) satisfies some mild regularity conditions, and provided k(0) is a P-matrix. Uniqueness follows under some further mild regularity conditions. An application to an impact problem is used to illustrate the theory.
