  Localized sufficient conditions for the large deviation principle of the
given stochastic differential equations will be presented for stochastic
differential equations with non-Lipschitzian and time-inhomogeneous
coefficients, which is weaker than those relevant conditions existing in the
literature. We consider at first the large deviation principle when
$\int_0^t\sup_{x\in\mathbb{R}^d}||\sigma(s,x)||\vee|b(s,x)|ds=:C_t<\infty$ for
any fixed $t$, then we generalize the conclusion to unbounded case by using
bounded approximation program.
