工程数学学报
工程數學學報
공정수학학보
CHINESE JOURNAL OF ENGINEERING MATHEMATICS
2013年
5期
751-755
,共5页
拟线性椭圆方程组%正弱解%上下解方法%存在性和不存在性
擬線性橢圓方程組%正弱解%上下解方法%存在性和不存在性
의선성타원방정조%정약해%상하해방법%존재성화불존재성
quasilinear elliptic systems%positive weak solution%method of upper and lower solutions%existence and nonexistence
本文研究了一类拟线性椭圆方程组在有界区域上的边值问题的正弱解的存在性和不存在性。利用方程组的特征值和特征函数分别构造了弱上解和弱下解，通过比较原理证明了弱下解小于弱上解，用上下解方法得到了正弱解的存在性。最后，用反证法证明了正弱解的不存在性，并给出了正弱解的不存在性条件。
本文研究瞭一類擬線性橢圓方程組在有界區域上的邊值問題的正弱解的存在性和不存在性。利用方程組的特徵值和特徵函數分彆構造瞭弱上解和弱下解，通過比較原理證明瞭弱下解小于弱上解，用上下解方法得到瞭正弱解的存在性。最後，用反證法證明瞭正弱解的不存在性，併給齣瞭正弱解的不存在性條件。
본문연구료일류의선성타원방정조재유계구역상적변치문제적정약해적존재성화불존재성。이용방정조적특정치화특정함수분별구조료약상해화약하해，통과비교원리증명료약하해소우약상해，용상하해방법득도료정약해적존재성。최후，용반증법증명료정약해적불존재성，병급출료정약해적불존재성조건。
In this paper, the existence and nonexistence of positive weak solutions for the quasilinear elliptic systems with boundary value problem in bounded domain are investigated. Firstly, we establish the weak upper and lower solutions of equations by the eigenvalue and eigenfunction, and prove that the weak lower is less than upper solutions by the comparison principle. Then according to the method of weak upper and lower solutions, we obtain the existence of positive weak solution for the systems. Finally, we derive the nonexistence of positive weak solutions by proof of contradiction, and give the nonexistence condition of positive weak solutions.
