On the classical and generalized solutions of boundary-value problems for difference-differential equations with variable coefficients

被引:0
作者
D. A. Neverova
A. L. Skubachevskii
机构
[1] Peoples’ Friendship University of Russia,
来源
Mathematical Notes | 2013年 / 94卷
关键词
difference-differential equation; first boundary-value problem; difference operator; Sobolev space;
D O I
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学科分类号
摘要
The first boundary-value problem for second-order difference-differential equations with variable coefficients on a finite interval (0, d) is considered. The following question is studied: Under what conditions will the boundary-value problem for a difference-differential equation have a classical solution for an arbitrary continuous right-hand side? It is proved that a necessary and sufficient condition for the existence of a classical solution is that certain coefficients of the difference operators on the orbits generated by the shifts be equal to zero.
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页码:653 / 667
页数:14
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