具有变系数梯度项的半线性椭圆型方程组解的存在性问题  

The Existence Problem of Solutions for Semilinear Elliptic Systems with Variable Coefficient Gradient Term

作　　者：任相霞[1] 

机构地区：[1]中国海洋大学数学科学学院,山东青岛266100

出　　处：《中国海洋大学学报（自然科学版）》2013年第3期113-116,共4页Periodical of Ocean University of China

摘　　要：本文研究一类包含变系数梯度项的半线性椭圆型耦合方程组解的存在性与不存在性问题。利用径向解方法、反证法和极值原理,得到了有界全局正解和整大解存在的充分必要条件及整大解和大解不存在的充分条件,找到了梯度项的加权系数对方程组解的影响。In this paper, we study the existence and nonexistence of solutions for semilinear elliptic sys-tems with variable coefficient gradient term. we give the necessary and sufficient conditions which ensure the existence of entire large solutions and entire bounded solutions, by using radial solution method, cont radicti-on method and extremum principle. We also obtain some appropriate sufficient conditions for the nonexistence of the large solutions and entire large solutions. We find the influence of the coefficient to the solutions of the systems.

关 键 词：大解 整大解 有界全局解 

分 类 号：O175[理学—数学]