An example of a nonunique solution of the Cauchy problem of Hamilton-Jacobi-Bellman (HJB) equation with surprisingly regular Hamiltonian is presented. The Hamiltonian H(t, x, p) is locally Lipschitz continuous with respect to all variables, convex in p and with linear growth with respect to p and x. The HJB equation possesses two distinct lower semicontinuous solutions with the same final conditions; moreover, one of them is the value function of the corresponding Bolza problem. The definition of lower semicontinuous solution was proposed by Frankowska (SIAM J. Control Optim. 31:257-272, 1993) and Barron and Jensen (Commun. Partial Differ. Equ. 15(12):1713-1742, 1990). Using the example an analysis and comparison of assumptions in some uniqueness results in HJB equations is provided.