文章基本信息

标题：A NEW EXISTENCE THEOREM FOR STURM-LIOUVILLE BOUNDARY VALUE PROBLEMS ON A MEASURE CHAIN
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作者：Zhao, Y.-H. ; Sun, Jian-Ping ; Yan, K.-M. 等
期刊名称：International Journal of Differential Equations and Applications
印刷版ISSN：1311-2872
出版年度：2003
卷号：7
期号：3
DOI：10.12732/ijdea.v7i3.1253
语种：English
出版社：International Journal of Differential Equations and Applications
摘要：In this paper we consider the following differential equation on a measurechain $T$\[u^{\Delta \Delta }(t)+f(u(\sigma (t)))=0,t\in [a,b]\cap T,\]satisfying Sturm-Liouville boundary value conditions\begin{eqnarray*}\alpha u(a)-\beta u^\Delta (a) &=&0, \\[12pt]\gamma u(\sigma (b))+\delta u^\Delta (\sigma (b)) &=&0.\end{eqnarray*}An existence result is obtained by using a Fixed Point Theorem due toKrasnoselskii and Zabreiko. Our conditions imposed on $f$ are very easy toverify and our result is even new for the special cases of differentialequations and difference equations, as well as in the general time scalesetting.
关键词：measure chain, solution of differential equation, fixed point;34B15, 39A10