On differential inequalities of S.A. Chaplygin related to limit Cauchy problem for sets of ordinary differential equations of first order

I.I. Bezvershenko

doi:10.15421/247723

On differential inequalities of S.A. Chaplygin related to limit Cauchy problem for sets of ordinary differential equations of first order

I.I. Bezvershenko (Dnipropetrovsk State University)

Abstract

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
$$\lim\limits_{x \rightarrow \infty} y(x) = y(\infty) = y_0, \; \lim\limits_{x \rightarrow \infty} z(x) = z(\infty) = z_0$$

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References

Chaplygin S.A. Collection of works, Vol. 1, OGIZ, 1948. (in Russian)

Mamedov Ya.D. "One-sided estimates in conditions of existence and uniqueness of solutions of limit Cauchy problem in Banach space", Siberian Math. J., 1965; U1(5): pp. 1190-1196. (in Russian)

Musaev V.M., Sardarly S.M. "Application of S.A. Chaplygin's method to limit Cauchy problem", Problems of Comp. Math., AN Azerb. SSR, 1967; 182-186. (in Russian)

Babkin B.N. "Aproximate integration of sets of ordinary differential equations of first order by S.A. Chaplygin's method", Izv. AN SSSR. Ser. Matem., 1954; 18(5): pp. 477-484. (in Russian)

Bezvershenko I.I. "On application of some modifications of S.A. Chaplygin's method to limit Cauchy problem", Ukrainian Math. J., 1971; 2: pp. 221-229. (in Russian)