Infinity Laplace Equation With Gradient Term And Nonlinear Inhomogeneous Term

In this paper we study the normalized infinity Laplace equation is a bounded domain, a ∈ R,We present some sufficient conditions on the inhomogeneous term f which used to guarantee the existence of solutions. Furthermore, we show for general f that there is a solution if the domain Ω is small, whereas the solution may fail to exist provided Ω large enough with f unchanging sign. In particular, we show that the gradient term has a substantial effect on the existence and nonexistence of solutions. Finally, we show the specific forms of the f to describe the conclusions. In addition, we give a clear description for the existence of positive solutions with where a threshold value for the coefficient of the gradient term is presented.Chapter 1 is to summarize the background and the development of the related issues and to briefly introduce the main results of this paper. In chapter 2, we give some definitions and auxiliary results as preliminaries. Then in chapter 3 we prove the main results.