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We prove a global existence result with initial data of low regularity, andprove the trend to the equilibrium for the Vlasov-Poisson-Fokker-Planck systemwith small non linear term but with a possibly large exterior confiningpotential in dimension $d=2$ and $d=3$. The proof relies on a fixed pointargument using sharp estimates (at short and long time scales) of thesemi-group associated to the Fokker-Planck operator, which were obtained by thefirst author.

On global existence and trend to the equilibrium for the Vlasov-Poisson-Fokker-Planck system with exterior confining potential