导　　师： 郭信康

学科专业： 070104

授予学位： 硕士

作　　者： ;

机构地区： 广西大学

摘　　要： 如今,由于在实践中的有着广泛应用,偏微分方程理论的研究飞速发展。而由于椭圆型方程的解有较好的性质,使其在偏微分方程研究中占有重要地位,一直受到更为广泛的研究。本文旨在对如下一类临界增长的拟线性退缩椭圆方程的Neumann问题的正解的多重性进行研究。 其中Ω /(?/)R~N是N维欧氏空间中的光滑有界区域,u≥0,2≤2α Now, for the broadly used in the practice, the theorem of partial differential equation be developed rapidly. And the character of the solutions of the elliptical partial differential equation is more kind, that make people to study it more broadly.In this paper we aims to study the Multiplicity of Positive Solutions for a Quasilinear Degenerated Elliptic Neumann Problem Involving Critical Sobolev Exponents as followingwhere Ω /(?/) R~N is the smooth boundary domain , u ≥ 0, 2 ≤ 2α < N, 0 < m <1, 2α < q~* - 1, q~* = /(2αN/)///(N-2a/) .The thesis is composed of two chapters. The first chapter devote to the summarize of the dissertation, we recount about the development, background and the present circumstance of the second order elliptic partial differential equation.Also, we recount about some results we have obtained in the past two years in this chapter.The second chapter is the primary proportion of this paper which composed of four sections. The 2.1 section is in order to direct discuss the problem in the followed section, we give the conditions we need.In the 2.2 section, we discuss the necessarily lemmas and their proofs.In the next section, we mainly investigate the week continuous property of with the help of concentration-compactness principle.In the last section, with the help of the lemmas and conclusions we have obtained in 2.2 and 2.3 section, and the help of mountain pass lemma, we discuss the existence of positive solution of the initial problem. And by the use of Eke-land Variational Principle, we can obtain another positive solution, that we have complete the proof.

关 键 词： 正解 临界增长 椭圆型方程

领　　域： [理学] [理学]