一类非线性椭圆方程组解的存在性  

Existence of solutions of a class of system of nonlinear elliptic equations

作　　者：章国庆[1] 刘三阳[1] 

机构地区：[1]西安电子科技大学理学院

出　　处：《西安电子科技大学学报》2004年第2期317-320,共4页Journal of Xidian University

基　　金：上海市高校青年科学基金资助项目(02GQ24);上海理工大学青年科研基金资助项目(X290)

摘　　要：将一类非线性椭圆方程组的求解问题化归为一给定泛函的临界点问题.利用变分法、经典的极值理论和山路引理证明了给定泛函在各种不同条件下临界点及非平凡临界点的存在性,从而得到了这类非线性椭圆方程组的解及非平凡解.In this paper, the solution of a class of system of nonlinear elliptic equations is transformed into a problem of finding critical points of the given functional. Under various conditions, the existence of critical points and nontrivial critical points is proved by using variational methods, the extreme theory and the Mountain Pass lemma, so that the solution and nontrivial solution of the nonlinear elliptic system is obtained.

关 键 词：非线性椭圆方程组 极值理论 山路引理 非平凡解 存在性 

分 类 号：O175.25[理学—数学]