A set-valued function, also called a correspondence or set-valued relation, is a mathematical function that maps elements from one set, the domain of the function, to subsets of another set. Set-valued functions are used in a variety of mathematical fields, including optimization, control theory and game theory. The set-valued functional differential equation has been widely applied in mathematics, physics, optimizations, optimal control, as well as economics and finance.[2, 3, 5, 6]. Here, we study the initial-value problem of a set-valued implicate functional differential equation with parameters. The existence of solution and its continuous dependence on parameters will be proved we study the existence of solutions of the parametric set-valued implicit functional differential equation The existence of solutions x ∈ C[0, T], C[0, T] is the Banach space of continuous functions defined on [0, T], will be proved. The continuous dependence of the solutions on the initial value x0 and the parameters γ. µ will be proved also.
saad, S., & Emharab, F. (2025). Existence and stability of the solution of an implicit set-valued functional differential equation with parameters. Electronic Journal of Mathematical Analysis and Applications, 13(2), 1-7. doi: 10.21608/ejmaa.2025.354162.1311
MLA
sooma saad; Fathi Emharab. "Existence and stability of the solution of an implicit set-valued functional differential equation with parameters", Electronic Journal of Mathematical Analysis and Applications, 13, 2, 2025, 1-7. doi: 10.21608/ejmaa.2025.354162.1311
HARVARD
saad, S., Emharab, F. (2025). 'Existence and stability of the solution of an implicit set-valued functional differential equation with parameters', Electronic Journal of Mathematical Analysis and Applications, 13(2), pp. 1-7. doi: 10.21608/ejmaa.2025.354162.1311
VANCOUVER
saad, S., Emharab, F. Existence and stability of the solution of an implicit set-valued functional differential equation with parameters. Electronic Journal of Mathematical Analysis and Applications, 2025; 13(2): 1-7. doi: 10.21608/ejmaa.2025.354162.1311
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