On the Asymptotic Properties of the Solutions of Some Functional Equations

Journal of Mathematical Sciences - Tập 229 - Trang 367-389 - 2018
D. V. Bel’skii1, G. P. Pelyukh1
1Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv, Ukraine

Tóm tắt

We establish new properties of the solutions of functional equations with constant delay and linearly transformed argument.

Tài liệu tham khảo

K. Mahler, “On a special functional equation,” J. London Math. Soc., 15, 115–123 (1940). D. V. Bel’skii and G. P. Pelyukh, “On the asymptotic properties of solutions of one functional-differential equation with linearly transformed argument,” Nelin. Kolyv., 16, No. 3, 291–313 (2013); English translation: J. Math. Sci., 201, No. 3, 263-287 (2014). J. Hale, Theory of Functional Differential Equations, Springer, New York (1977). N. G. de Bruijn, “The asymptotically periodic behavior of the solutions of some linear functional equations,” Amer. J. Math., 71, No. 2, 313–330 (1949). I. S. Berezin and N. P. Zhidkov, Numerical Methods [in Russian], Vol. 1, Fizmatgiz, Moscow (1962). G. P. Pelyukh and D. V. Bel’skii, “On the asymptotic properties of the solutions of a linear functional-differential equation of neutral type with constant coefficients and linearly transformed argument,” Nelin. Kolyv., 15, No. 4, 466–493 (2012); English translation: J. Math. Sci., 194, No. 4, 374–403 (2013).