Existence of extremal solutions for discontinuous Stieltjes differential equations

Journal of inequalities and applications

article

Rodrigo López Pouso¹  Ignacio Márquez Albés¹ 

[1] Faculty of Mathematics, Universidade de Santiago de Compostela

关键词: Upper solution;    Ordinary differential equations;    Impulsive differential equations;    Dynamic equations;    Time scales;   

DOI  :  10.1186/s13660-020-02316-w

学科分类：电力

来源: SpringerOpen

【 摘 要 】

Stieltjes differential equations, which contain equations with impulses and equations on time scales as particular cases, simply consist in replacing usual derivatives by derivatives with respect to a nondecreasing function. In this paper we prove new results for the existence of extremal solutions for discontinuous Stieltjes differential equations. In particular, we prove that the pointwise infimum of upper solutions of a Stieltjes differential equation is the minimal solution under certain hypotheses. These results can be adapted to the context of both difference equations and impulsive differential equations.

【 授权许可】

CC BY