Solutions and Positive Solution of a Class of Second-Order Singular Quasilinear Equations

The solution and positive solution are considered for a class of second-order quasilinear equations with first derivative,where the nonlinear term is allowed to be singular.By constructing suitable Banach space and applying corresponding integral equation,two local existence theorems are established. The theorems show that the existence of solution and positive solution depends upon the "height" of principal part of nonlinear term on a bounded set.