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This paper is devoted to the $L^p$ ($p>1$) solutions of one-dimensionalbackward stochastic differential equations (BSDEs for short) with general timeintervals and generators satisfying some non-uniform conditions in $t$ and$\omega$. An existence and uniqueness result, a comparison theorem and anexistence result for the minimal solutions are respectively obtained, whichconsiderably improve some known works. Some classical techniques used to dealwith the existence and uniqueness of $L^p$ ($p>1$) solutions of BSDEs withLipschitz or linear-growth generators are also developed in this paper.

$L^p\ (p>1)$ solutions of BSDEs with generators satisfying some non-uniform conditions in $t$ and $\omega$