三阶差分方程边值问题

【作者】 杨春明；

【导师】 翁佩萱；

【作者基本信息】 华南师范大学 ， 应用数学， 2004， 硕士

【摘要】 本文首先研究了三阶非线性差分方程： Δ~3u(t-2)+a(t)f(u(t))=0，t∈[2，T+2]， 满足多种边界条件时的正解存在性和二解性，其次研究了特征值问题： Δ~3u(t-2)+λα(t)f(u(t))=0，t∈[2，T+2]， 在满足不同边界条件时正解的存在性及二解性。我们给出了各自边值问题的Green函数的具体表达式，使正解存在性及二解性的判断较为方便。并且分别举例说明定理的应用。更多还原

【Abstract】 Firstly,some criteria for the existence of at least one positive solution and two positive solutions are obtained respectively for the third-order nonlinear difference equation:satisfying several different types of boundary conditions. The second part is devoted to determine values of A for which there exist at least one positive solution and two positive solutions forsatisfying several different types of boundary conditions. We have presented different function expression of Green functions. So the judgement of the existence on one pos-itive solution and two positive solutions becomes convenient. At last,many examples have given to demonstrate the applications of our theorems.更多还原