  In this paper, we study the existence, uniqueness and comparison theorems for
solutions of one-dimensional reflected backward stochastic differential
equations (RBSDEs) with one continuous obstacle and backward stochastic
differential equations (BSDEs). The generators of such RBSDEs and BSDEs have a
quadratic growth in $z$, with the quadratic term taking the form $f(y)|z|^2$,
where the function $f$ is defined on an open interval $D$ and locally
integrable. The terminal random variables (and obstacles) of such RBSDEs and
BSDEs are unbounded. Our proofs mainly depend on a transformation based on $f$
and the domination arguments. As applications, we give a probabilistic
interpretation of an obstacle problem for a quadratic PDE with continuous
coefficient, whose solution takes values in $D$, and study an optimal stopping
problem for the payoff of American options.
