Existence And Energy Estimate Of Singular Positive Solutions For Quasilinear Elliptic Equation

In this paper, our main purpose is to establish the existence of singular positive solutions of second order quasilinear elliptic equations with super and lower solution method. On the other hand, we will also prove that the energy of positive solutions for quasi-linear elliptic equations with Dirichlet problem on the unit ball is uniformly bounded. We also prove that if positive regular solutions convergences to a singular solution pointwise in (0,1), then the convergences obtain in L^q+1 and H¹ as well. The main contents are as follows:In chapter 2, we proved that there exists infinitely many singular positive radial solutions which satisfy a priori estimates for quasilinear elliptic equations.In chapter 3, we study the energy estimate of singular positive solutions for a class quasilinear elliptic equations. We also prove that if positive regular solutions convergences to a singular solution pointwise in (0,1), then the convergences obtain in L^q+l and H¹ as well.The above results are the improvement and complement of the corresponding partly results had been given by [10,11,33]...