Bounded solutions, Lp(p>1) solutions and L1L1 solutions for one dimensional BSDEs under general assumptions

This paper aims at solving one dimensional backward stochastic differential equations (BSDEs) under weaker assumptions. We establish general existence, uniqueness, and comparison results for bounded solutions, Lp(p>1) solutions and L1L1 solutions of the BSDEs. The time horizon is allowed to be finite or infinite, and the generator gg is allowed to have a general growth in yy and a quadratic growth in zz. As compensation, the generator gg needs to satisfy a kind of one-sided linear or super-linear growth condition in yy, instead of the monotonicity condition in yy as is usually done. Many of our results improve considerably some known results, even though for the case of finite time horizon and the case of L2L2 solution.