Computational fixed-point theory for differential delay equations with multiple time lags
The authors consider the problem of existence of periodic solutions of differential delay equations with multiple time lags. Using an original and elaborated construction they find an equivalent fixed point operator equation. An appropriate notion of radii polynomials is defined, which is used in the hypothesis of some result that prove the unique solvability of the fixed point operator equation mentioned before. The contraction mapping theorem is used at this step. For a certain class of differential delay equations with multiple time lags the authors provide an explicit construction of the radii polynomials. For this, one needs to find numerical approximations of periodic solutions using Newton's method applied on a finite dimensional projection. At the end, two applications are provided. The coexistence of three periodic solutions for a given delay equation with two time lags is obtained. The second application provides rigorous computations of several nontrivial periodic solutions for a delay equation with three time lags.
scientific article; zbMATH DE number 6012780
scientific article