This paper is devoted to the L p (p > 1) solutions of one-dimensional backward stochastic differential equations (BSDEs for short) with general time intervals and generators satisfying some non-uniform conditions in t and ω. An existence and uniqueness result, a comparison theorem and an existence result for the minimal solutions are respectively obtained, which considerably improve some known works.Some classical techniques used to deal with the existence and uniqueness of L p (p > 1) solutions of BSDEs with Lipschitz or linear-growth generators are also developed in this paper.