Solvability of non-semicontinuous systems of Stieltjes differential inclusions and equations

Advances in Difference Equations

article

López Pouso, Rodrigo¹  Márquez Albés, Ignacio¹  Rodríguez-López, Jorge¹ 

[1] Departamento de Estatística, Análise Matemática e Optimización Instituto de Matemáticas, Universidade de Santiago de Compostela

关键词: Differential inclusions;    Discontinuous differential equations;    Stieltjes differential inclusions;    Stieltjes differential equations;   

DOI  :  10.1186/s13662-020-02685-y

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

We prove an existence result for systems of differential inclusions driven by multivalued mappings which need not assume closed or convex values everywhere, and need not be semicontinuous everywhere. Moreover, we consider differentiation with respect to a nondecreasing function, thus covering discrete, continuous and impulsive problems under a unique formulation. We emphasize that our existence result appears to be new even when the derivator is the identity, i.e. when derivatives are considered in the usual sense. We also apply our existence theorem for inclusions to derive a new existence result for discontinuous Stieltjes differential equations. Examples are given to illustrate the main results.

【 授权许可】

CC BY