Infinite time interval backward stochastic differential equations with continuous coefficients

In this paper, we study the existence theorem for [Formula: see text] [Formula: see text] solutions to a class of 1-dimensional infinite time interval backward stochastic differential equations (BSDEs) under the conditions that the coefficients are continuous and have linear growths. We also obtain the existence of a minimal solution. Furthermore, we study the existence and uniqueness theorem for [Formula: see text] [Formula: see text] solutions of infinite time interval BSDEs with non-uniformly Lipschitz coefficients. It should be pointed out that the assumptions of this result is weaker than that of Theorem 3.1 in Zong (Turkish J Math 37:704-718, 2013).