Bifurcation Problems for a Class of Degenerate Quasilinear Elliptic Equations  

作　　者：Yun-xiang Li Yu Ye Fang-li Xia 

机构地区：[1]Department of Mathematics, Hunan City University, Yiyang 413049, China [2]Department of Mathematics, Changsha University of Science and Technology, Changsha 410076, China [3]Department of Mathematics, Central South University, Changsha 410075, China

出　　处：《Acta Mathematicae Applicatae Sinica》2010年第3期395-404,共10页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China (No. 10671211)

摘　　要：In this paper we consider the bifurcation problem -div A（x, u）=λa（x）｜u｜^p-2u＋f（x,u,λ） in Ω with p 〉 1.Under some proper assumptions on A（x,ξ）,a（x） and f（x,u,λ）,we show that the existence of an unbounded branch of positive solutions bifurcating Irom the principal eigenvalue of the problem --div A（x, u）=λa（x）｜u｜^p-2u.In this paper we consider the bifurcation problem -div A（x, u）=λa（x）｜u｜^p-2u＋f（x,u,λ） in Ω with p 〉 1.Under some proper assumptions on A（x,ξ）,a（x） and f（x,u,λ）,we show that the existence of an unbounded branch of positive solutions bifurcating Irom the principal eigenvalue of the problem --div A（x, u）=λa（x）｜u｜^p-2u.

关 键 词：Quasilinear elliptic equation BIFURCATION principal eigenvalue 

分 类 号：O175.25[理学—数学] O177.91[理学—基础数学]