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The paper develops the needle variations technique in application to a class of infinite-horizon optimal control problems in which an appropriate relation between the growth rate of the solution and the growth rate of the objective function is satisfied. The optimal objective value does not need to be finite. Based on the concept of weakly overtaking optimality, we establish the normal form version of the Pontryagin maximum principle with an explicitly specified adjoint variable. A fewdoi:10.1090/conm/619/12381 fatcat:eevroqxgqrfpji2hi4bb5wuai4