Existence Of Solutions For Singular Quasilinear Elliptic Equation

we discuss the following p(x)-Laplacian Dirichlet problemby sub-supersolution methods, here f(x, t) may be singular at t=0.The operator△_p(x)u is said to be p(x)-Laplacian, which becomes pLaplacian when p(x)=p (a constant).Firstly, when p(x)=p is a constant, we study the existence of positive weak solutions for problem (*). We get three theorems which extend R.P.Agarwal [2] and D.D.Hai [4] respectivly.Secondly, when p(x) is continuous function on (?), we discuss problem (*) and get four theorems. These theorems extend R.P.Agarwal [2] and K.Perera[15] respectivly. The discussion is based on the theory of the spaces L^p(x)(Ω) and W^{k, p(x)}(Ω).