摘要
研究一类二阶差分方程Δ2y(k-1)+f(k,y(k))=0,k∈[1,T]在混合边值条件y(0)=0,Δy(T)=0下正解的存在性.应用临界点理论中的山路引理,当非线性项在0点及无穷远点为超线性增长时和与其等价的条件下,得到上述边值问题至少一个正解的存在性.最后通过一个例子说明定理结论的有效性.
This paper mainly deals with the existence of the positive solution of the second-order discrete system Δ2y(k-1)+f(k,y(k))=0,k∈Z.With the mixed bound ary conditions y(0)=0,Δy(T)=0 and the facts that f(k,y) is superlinear both at 0 and at infinity,at least one positive solution is obtained by using the mountain pass theorem of the critical point theorem.Finally,by one example we show that the theorems which we get in this paper are meanful.
出处
《广州大学学报（自然科学版）》
CAS
2009年第2期45-48,共4页
Journal of Guangzhou University:Natural Science Edition
基金
广东省自然科学基金资助项目(06021578)
广州市属高校科技计划项目(62006)
关键词
二阶差分方程
混合边值问题
正解
临界点理论
second-order difference equation
mixed boundary value problems
positive solution
critical point.
