Green's function for first-order multipoint boundary value problems and applications to the existence of solutions with constant sign

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:388

Article

Nieto, Juan J.¹  Rodriguez-Lopez, Rosana¹ 

[1] Univ Santiago de Compostela, Fac Matemat, Dept Anal Matemat, Santiago De Compostela 15782, Spain

关键词: First-order differential equations;    Linear differential equations;    Boundary value problems;    Existence of solution;    Uniqueness of solution;    Explicit solution;    Green's function;    Positive solutions;   

DOI  :  10.1016/j.jmaa.2011.10.037

来源: Elsevier

【 摘 要 】

We consider a first-order linear differential equation subject to boundary value conditions which take into account the values of the function at multiple points in the interval of interest. For this problem, we calculate the Green's function which allows to express in integral form the exact expression of the unique solution to the multipoint boundary value problem under the appropriate conditions. From this study, some results are derived concerning the existence of solutions with a constant sign (that is, some comparison results for first-order multipoint boundary value problems). (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free