After a brief survey of the literature about sufficient conditions, we givedifferent sufficient conditions of optimality for infinite-horizon calculusof variations problems in the general (non concave) case. Some sufficientconditions are obtained by extending to the infinite-horizon setting thetechniques of extremal fields. Others are obtained in a specialqcase of reduction to finite horizon. The last result uses auxiliaryfunctions. We treat five notions of optimality. Our problems are essentiallymotivated by macroeconomic optimal growth models.
