Existence of solutions of first-order differential equations via a fixed point theorem for discontinuous operators

Fixexd point theory and applications

Rubé¹  n Figueroa Sestelo²  Rodrigo Ló³  pez Pouso⁴ 

[1] Departamento de Análise Matemática, Facultade de Matemáticas, Universidade de Santiago de Compostela, Santiago de Compostela, Spain

关键词: Point Theorem;    Fixed Point Theorem;    Bounded Variation;    Continuous Solution;    Extremal Solution;   

DOI  :  10.1186/s13663-015-0472-5

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We use a recent Schauder-type result for discontinuous operators in order to look for solutions for first-order differential equations subject to initial functional conditions. We show how this abstract fixed-point result allows us to consider a nonlinearity which can be strongly discontinuous. Some examples of applications and comparison with recent literature are included.

【 授权许可】

CC BY