Some consequences of an existence result by Kiguradze and Partsvania for singular Dirichlet problems

Boundary value problems

Rodrigo Lpez Pouso¹  Rubn Figueroa² 

[1] Department of Mathematical Analysis, University of Santiago de Compostela, Spain;Department of Specific Didactics, University of Burgos, Burgos, Spain

关键词: discontinuous differential equations;    singular differential equations;    functional differential equations;    boundary value problems;    equations with delay;    equations with advance;   

DOI  :  10.1186/s13661-014-0160-0

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

A sharp theorem by Kiguradze and Partsvania ensures the existence of extremal solutions between given lower and upper solutions for singular Dirichlet problems. This paper has a twofold purpose: first, we present a new sufficient condition for one of Kiguradze and Partsvania’s assumptions, and we illustrate its applicability in the study of a new family of examples; second, we combine Kiguradze and Partsvania’s theorem with Heikkilä’s iterative technique to obtain a new result on the existence of extremal solutions for a more general class of discontinuous and singular functional boundary value problems. In particular, our framework includes classical equations with delay (or advance), singularities with respect to the independent variable, and implicit functional boundary conditions. MSC: 34A12, 34A36.

【 授权许可】

CC BY