Extremal solutions to differential equations with singular p(t)-Laplacian

We consider positive solutions of the nonlinear differential equations [Formula: see text] involving singular [Formula: see text]-Laplacian, i.e. [Formula: see text] and [Formula: see text] as [Formula: see text]. Sufficient conditions are given for the existence and nonexistence of extremal solutions, which do not appear in the case where [Formula: see text] for some constant [Formula: see text]. Furthermore, we investigate the asymptotic properties of the extremal solutions, and give some examples to illustrate our results.