We establish a composition theorem of Stepanov almost periodic functions, and, with its help, a composition theorem of Stepanov-like pseudo almost periodic functions is obtained. In addition, we apply our composition theorem to study the existence and uniqueness of pseudo-almost periodic solutions to a class of abstract semilinear evolution equation in a Banach space. Our results complement a r...

Hybrid automata provide a language for modeling and analyzing digital and analogue computations in real-time systems. Hybrid automata are studied here from a dynamical systems perspective. Necessary and sufficient conditions for existence and uniqueness of solutions are derived and a class of hybrid automata whose solutions depend continuously on the initial state is characterized. The results ...

in this article, we investigate sufficient conditions for existence of maximal and minimalsolutions to a coupled system of highly nonlinear differential equations of fractional order with mixedtype boundary conditions. to achieve this goal, we apply monotone iterative technique togetherwith the method of upper and lower solutions. also an error estimation is given to check theaccuracy of the me...

In this paper, by using the w-compatible conditions of mapping pair, we discuss the existence and uniqueness problem of the common coupled fixed point for mappings defined on a set equipped with two rectangular b-metrics. Some new common coupled fixed point theorems are obtained. We also provide illustrative examples in support of our new results. As application, we provide an existence and uni...

Background : The teaching of differential equations is dominated by an excessively algebraised analytic tradition. For this reason, studies that contribute to conceptualising mathematical objects associated with the equation are important, particularly existence and uniqueness theorem. Objectives From its genesis, objective analyse nature knowledge, epistemology from practice. We give account v...

*Correspondence: [email protected] College of Mathematics and Computer Science, Fuzhou University, Fuzhou, 350116, P.R. China Abstract Choosing space Cg as the phase space, the existence, uniqueness and stability of the solution to neutral stochastic functional differential equations with infinite delay (short for INSFDEs) are studied in this paper. Under non-Lipschitz condition, weakened ...

In this paper, we study the existence and uniqueness of solution (EUS) as well as Hyers-Ulam stability for a coupled system of FDEs in Caputo’s sense with nonlinear p-Laplacian operator. For this purpose, the suggested coupled system is transferred to an integral system with the help of four Green functions G1 (t, s), G1 (t, s), G2 (t, s), G2 (t, s). Then using topological degree theory and Ler...