Solutions of sturm-liouville boundary value problems for higher-order differential equations

被引：4

作者：

Liu Y. ^{[1
,2
]}

机构：

[1] Department of Mathematics, Guangdong University of Business Studies, Guangzhou, Guangdong

来源：

Journal of Applied Mathematics and Computing | 2007年 / 24卷 / 1-2期

关键词：

Higher order differential equation; Positive solution; Solution; Sturm-Liouville boundary value problem;

D O I：

10.1007/BF02832313

中图分类号：

学科分类号：

摘要：

The existence of solutions of a class of two-point boundary value problems for higher order differential equations is studied. Sufficient conditions for the existence of at least one solution are established. It is of interest that the nonlinearity f in the equation depends on all lower derivatives, and the growth conditions imposed on f are allowed to be super-linear (the degrees of phases variables are allowed to be greater than 1 if it is a polynomial). The results are different from known ones since we don't apply the Green's functions of the corresponding problem and the method to obtain a priori bound of solutions are different enough from known ones. Examples that can not be solved by known results are given to illustrate our theorems. © 2007 Korean Society for Computational & Applied Mathematics and Korean SIGCAM.

引用

页码：231 / 243

页数：12

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