On the Existence and Uniqueness of Periodic Solutions of Differential Delay Equations.
We study the existence of global canard surfaces for a wide class of real singular perturbation problems. These surfaces define families of solutions which remain near the slow curve as the singular parameter goes to zero.
For several specific mappings we show their chaotic behaviour by detecting the existence of their transversal homoclinic points. Our approach has an analytical feature based on the method of Lyapunov-Schmidt.
We study the vector -Laplacian We prove that there exists a sequence of solutions of () such that is a critical point of and another sequence of solutions of such that is a local minimum point of , where is a functional defined below.
We study the existence of one-signed periodic solutions of the equations where , is continuous and 1-periodic, is a continuous and 1-periodic in the first variable and may take values of different signs. The Krasnosielski fixed point theorem on cone is used.
The stability properties of solutions of the differential system which represents the considered model for the Belousov - Zhabotinskij reaction are studied in this paper. The existence of oscillatory solutions of this system is proved and a theorem on separation of zero-points of the components of such solutions is established. It is also shown that there exists a periodic solution.
The paper investigates the singular initial problem[4pt] [4pt] on the half-line . Here , where , and are zeros of , which is locally Lipschitz continuous on . Function is continuous on , has a positive continuous derivative on and . Function is continuous on and positive on . For specific values we prove the existence and uniqueness of damped solutions of this problem. With additional conditions for , and it is shown that the problem has for each specified a unique...