Open AccessOn differential inequalities of S.A. Chaplygin related to limit Cauchy problem for sets of ordinary differential equations of first order
Author(s) -
I. I. Bezvershenko
Publication year - 2021
Publication title -
researches in mathematics
Language(s) - English
Resource type - Journals
eISSN - 2664-5009
pISSN - 2664-4991
DOI - 10.15421/247723
Subject(s) - limit (mathematics) , ordinary differential equation , order (exchange) , mathematics , cauchy distribution , mathematical analysis , cauchy problem , pure mathematics , differential equation , mathematical physics , initial value problem , combinatorics , finance , economics
We prove a theorem on differential inequalities related to limit Cauchy problem for the set of ordinary differential equations$$y' = f(x,y,z),$$z' = \varphi(x,y,z)$$with boundary conditions$$\lim\limits_{x \rightarrow \infty} y(x) = y(\infty) = y_0, \; \lim\limits_{x \rightarrow \infty} z(x) = z(\infty) = z_0$$