Pointwise conditions in discrete boundary value problems with nonlocal boundary conditions

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• 作者：Christopher S. Goodrich ^{cgood@prep.creighton.edu}
• 关键词：Summation equation ; Coercivity ; Discrete calculus ; Positive solution ; Nonlocal boundary value problem
• 刊名：Applied Mathematics Letters
• 出版年：2017
• 出版时间：May 2017
• 年：2017
• 卷：67
• 期：Complete
• 页码：7-15
• 全文大小：771 K
• 卷排序：67

文摘

We consider summation equations having the form y(t)=γ(t)H∑i=1nαiyξi+λ∑s=0bG(t,s)f(s,y(s+1)).By utilizing a new order cone, we are able to demonstrate the existence of at least one positive solution of the equation in the case where only pointwise conditions are imposed on the function HH. This is in contrast to usual approach of employing either asymptotic or interval-type conditions on this function. Finally, we provide some applications of the abstract result to discrete boundary value problems with nonlocal boundary conditions.