Weakly Nonlinear Boundary-Value Problems for Operator Equations in Banach Spaces

被引：0

作者：

Zhuravliov V.P. ^{[1
]}

机构：

[1] Polissya National University, Staryi Ave., 7, Zhytomyr

来源：

Journal of Mathematical Sciences | 2023年 / 270卷 / 2期

关键词：

D O I：

10.1007/s10958-023-06345-w

中图分类号：

学科分类号：

摘要：

We consider weakly nonlinear boundary-value problems for operator equations with generalized invertible operator in the linear part of the boundary-value problem in the critical case. We establish necessary and sufficient conditions for the existence of at least one and unique solution of this boundary-value problem and propose convergent iterative procedures for its construction. © 2023, Springer Nature Switzerland AG.

引用

页码：263 / 279

页数：16

共 17 条

[1]

Lyapunov A.M., General Problem of Stability of Motion [In Russian], (1950)

[2]

Grebennikov E.A., Ryabov Y.A., Constructive Methods in the Analysis of Nonlinear Systems [In Russian], (1979)

[3]

Boichuk A.A., Constructive Methods in the Analysis of Boundary-Value Problems [in Russian], Naukova Dumka, Kiev, (1990)

[4]

Boichuk A.A., Zhuravlev V.F., Samoilenko A.M., Generalized Inverse Operators and Noetherian Boundary-Value Problems [in Russian], Institute of Mathematics, Ukrainian National Academy of Sciences, Kiev, (1995)

[5]

Boichuk A.A., Zhuravlev V.F., Samoilenko A.M., Linear Noetherian boundary-value problems for impulsive differential systems with delay, Differents. Uravn., 30, 10, pp. 1677-1682, (1994)

[6]

Boichuk O.A., Panasenko E.V., Weakly nonlinear boundary-value problems for differential equations in a Banach space in the critical case, Nelin. Kolyv, 13, No. 4,, pp. 483-496, (2010)

[7]

Krein S.G., (1972)

[8]

Zhuravlev V.F., Weakly nonlinear boundary-value problems for the Fredholm integral equations with degenerate kernels in Banach spaces, Nelin. Kolyv., 21, 3, pp. 347-357, (2018)

[9]

Boichuk A.A., Zhuravlev V.F., Samoilenko A.M., Normally Solvable Boundary-Value Problems [In Russian], (2019)

[10]

Zhuravlev V.F., Fomin N.P., Zabrodskiy P.N., Conditions of solvability and representation of the solutions of equations with operator matrices,” Ukr. Mat. Zh., 71, No 4, 471–485 (2019)

← 1 2 →