带奇异权函数的竞争型边界爆破椭圆方程组解的性质  

Properties of Boundary Blow-up Solutions to Elliptic Systems of Competitive Type with Singular Weights

作　　者：黄水波[1] 田巧玉[1] 穆春来[2] 

机构地区：[1]合作民族师范高等专科学校数学系,甘肃合作747000 [2]重庆大学数理学院,重庆400030

出　　处：《工程数学学报》2009年第3期547-552,共6页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10771226);重庆市自然科学基金(CQCSTC2007BB0124)

摘　　要：利用爆破上、下解方法,本文建立了带奇异权函数的竞争型椭圆方程组正的边界爆破解的存在性和边界行为,这里奇异权函数可以在边界的某一部分有界,而在其他的部分趋于无穷或者震荡。特别是在没有准确的边界行为的条件下,得到了爆破解的唯一性。结果表明为了得到唯一性,并不需要权函数精确的边界行为,而只需要控制其在边界附近的行为即可。Using the method of blow up lower and upper solutions, the existence and boundary behavior of positive boundary blow up solutions for some elliptic systems of competitive type with singular weight functions are obtained, here the singular weight functions are permitted to be bounded in some parts of the boundary, and to go to infinity or even oscillate in other parts. Furthermore, the uniqueness of the boundary blow up solutions without the exact boundary behavior are also studied. The results show that it is not necessary to impose an exact boundary behavior to the weight functions, but only to control their growth near the boundary for uniqueness.

关 键 词：边界爆破解 奇异权函数 爆破上、下解方法 

分 类 号：O175.25[理学—数学]