一类拟线性椭圆方程3个非平凡解的存在性  

The Existence of Three Nontrivial Solutions for a Class of Quasi-Linear Elliptic Equations

作　　者：储昌木[1] 

机构地区：[1]贵州民族大学理学院,贵阳550025

出　　处：《西南大学学报（自然科学版）》2012年第12期114-118,共5页Journal of Southwest University(Natural Science Edition)

基　　金：贵州省科教青年英才培养工程项目(黔省专合字(2012)157号);贵州省"模式识别与智能系统"重点实验室建设项目(黔科合计[2009]4002)

摘　　要：通过截断技术和涉及第二形变引理的变分方法研究了一类不含任何增长条件的拟线性椭圆方程3个非平凡解的存在性.首先利用截断技术和变分技巧得到该类拟线性椭圆方程存在1个非负非平凡解和1个非正非平凡解,然后通过第二形变引理构造这两个非平凡解之间的特殊山路,最后应用山路引理获得该类拟线性椭圆方程第三个非平凡解的存在性.Using the truncation technique and the variational approach involving the second deformation lemma, the existence of three nontrivial solutions for a class of quasi-linear elliptic equations without any growth conditions is obtained. First, through the truncation technology and the variational technique, we obtain that the elliptic equations have a nonnegative nontrivial solution and a nonpositive nontrivial solu- tion. Subsequently, we use the second deformation lemma to construct a special mountain pass path be- tween the two nontrivial solutions and obtain the existence of a third nontrivial solution by the mountain pass lemma.

关 键 词：拟线性椭圆方程 截断技术 变分方法 第二形变引理 

分 类 号：O176.3[理学—数学]