The Existence Of Entropy Solutions To Noncoercive Nonlinear Elliptic Equations With Measure Data

In this article,we are interested in existence of entropy solutions of quasilinear elliptic problems with principal part having degenerate.Let ?(?)RN be a bounded domain.The model case iswhere p is a real number such that 2-1/N<p<N,c(x)?N/Lp-1,r(?),N/p-1?r?+?,b(x)?LN,1(?),? is a diffuse measure.0 ??<1.In chapter 1,we introduce the research status of the priori problems at home or abroad and our main results.In chapter 2,we introduce some notations,measures,Lorentz space and the research methods used in this paper.In chapter 3,we consider approximate problems via priori estimate of |?u|p-1 in LN',?(n).In chapter 4,we proved the existence of entropy solutions of quasilinear elliptic problems.