  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
$\omega$. 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.
