In this paper, we study the existence of periodic solutions of the nonlinear system of integro-differential equationsIn the process we use the fundamental matrix solution to convert the given integro-differential equation into an equivalent integral equation.Then by using Krasnoselskii's fixed point theorem we obtain the existence of periodic solution and by contraction mapping principle we obtain the uniqueness. An application in two dimension is given.2010 Mathematics Subject Classification. 34A34, 35K13, 45J05, 47H10.
Abstract. In this paper, we study the existence of periodic and nonnegative periodic solutions of the nonlinear neutral differential equationWe invert this equation to construct a sum of a completely continuous map and a large contraction which is suitable for applying the modification of Krasnoselskii's theorem. The Caratheodory condition is used for the functions Q and G.
In this article, we consider a nonlinear neutral q-fractional difference equation. So, we apply the fixed point theorem of Krasnoselskii to obtain the existence of solutions under sufficient conditions. After that, we use the fixed point theorem of Banach to show the uniqueness, as well as the stability of solutions. Our main results extend and generalize previous results mentioned in the conclusion.
There is great focus on phenomena that depend on their past history or their past state. The mathematical models of these phenomena can be described by differential equations of a self-referred type. This paper is devoted to studying the solvability of a state-dependent integro-differential inclusion. The existence and uniqueness of solutions to a state-dependent functional integro-differential inclusion with delay nonlocal condition is studied. We, moreover, conclude the existence of solutions to the problem with the integral condition and the infinite-point boundary one. Some properties of the solutions are given. Finally, two examples illustrating the main result are presented.
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