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In this paper we prove a comparison result between semicontinuousviscosity subsolutions and supersolutions to Hamilton-Jacobi equations of the form $u_t+H(x,Du) = 0$ 
in ${\rm I}\!{\rmR}^n\times(0,T)$ 
where the Hamiltonian H may be noncoercive inthe gradient Du. As a consequence of the comparison result and the Perron's method we get the existence of a continuous solution of this equation.
