The Existence Of Solution For Nonlinear Elliptic Differential Equations

In this paper, we use the theory and methods of nonlinear functional analysis to deal with the existence of the solutions for p(x)-Laplace equations under Dirichlet boundary value and periodic boundary value conditions. We consider the case that p(x) is constant and p(x)(x??(?)RN) is radially symmetric, respectively.The main content of this paper is divided into two chapters:In chapter 2, when p(x)=p is a constant, we mainly discussed the existence of solutions for elliptic problems: where ? is a smooth bounded domain in RN, f(x,t) is a Caratheodory function and satisfying some construct conditions. This paper improves the work of zhang jihong and zhang shengui in [6] and [9].In chapter 3, when p(x) is continuous function on ?, we discuss the following problem with nontrivial solutions: where ? is a bounded domain in RN, p(x) is a Lipschitz continuous function and p(x)>1, x??, f(x,t) is a continuous function and satisfy some of the critical conditions for growth. This paper improves part of the work of zhang qihu in [17].