Existence And Regularity Results Of A Class Of Singular P-laplacian Equations

In this paper, we study the existence and regularity of solutions to the following singular p-laplacian elliptic problemBy approximation method, we prove the existence of the approximate solution and its priori estimate, and then by weak convergence method, we prove the existence and regularity of solutions to problem (P1).The main content is divided into four chapters. In chapter one, we describe the back-ground of the problems, and then we briefly recall some related results about the semilinear or quasilinear elliptic equations which were published in the past few years. At the end of this chapter, we state our problems and sketch the methods and the techniques to be used. In chapter two, some definitions, lemmas and symbols which will be used in this paper are given. Our main results and its proof can be found in chapter three and chapter four. In chapter three, we prove the existence and regularity results of problem (P1) with0<μ<CN,p. In chapter four, we prove the existence and regularity results of problem (P1) with μ< 0.