Investigations in the theory of bounded and periodic solutions of differential equations

Мухамадиев, Э. М.

doi:10.1007/bf01141630

Cited by 18 publications

(14 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…where A is the same linear continuous operator as in (2). The statement below is the main result of the present paper.…”

Section: Object Of Investigation and Main Resultsmentioning

confidence: 89%

“…Let dim E < C1: For Eq. (2) to have at least one solution x 2 C 1 .R; E/ for arbitrary h 2 C 0 .R; E/ and K 2 K; it is necessary and sufficient that the operator LW C 1 .R; E/ ! C 0 .R; E/ have a continuous inverse.…”

Section: Object Of Investigation and Main Resultsmentioning

confidence: 99%

“…These operators were studied in [2][3][4][5][6][7][8][9], etc. The definition of c-continuous operator that uses locally convergent sequences was proposed by the author (see, e.g., [10][11][12]).…”

Section: Main Functional Spaces and C-continuous Operatorsmentioning

confidence: 99%

See 2 more Smart Citations

Conditions for the existence of bounded solutions of nonlinear differential and functional differential equations

Slyusarchuk

2010

Ukr Math J

View full text Add to dashboard Cite

Let E be a finite-dimensional Banach space, let C 0 .R; E/ be a Banach space of functions continuous and bounded on R and taking values in E; let KW C 0 .R; E/ ! C 0 .R; E/ be a c-continuous bounded mapping, let AW E ! E be a linear continuous mapping, and let h 2 C 0 .R; E/: We establish conditions for the existence of bounded solutions of the nonlinear equation Main Functional Spaces and c-Continuous OperatorsLet R be the set of all real numbers, let C be the set of all complex numbers, let E be a real or complex Banach space with norm k k E ; and let L.E; E/ be the Banach algebra of all linear continuous operators AW E ! E with the normBy C 0 .R; E/ we denote the Banach space of functions x D x.t/ continuous and bounded on R and taking values in E with the normNote that kak E D jaj if E D R or E D C: Let C 1 .R; E/ denote the Banach space of functions x 2 C 0 .R; E/ each derivative of which is an element of the space C 0 .R; E/ with the normWe say that a sequence .x n / n 1 of elements of the space C 0 .R; E/ converges locally to an element x 2 C 0 .R; E/ and write x n loc: C 0 .R;E / ! x as n ! 1 if this sequence is bounded and, for every number p > 0; one has National University of Water Management and Nature Resources Use, Rivne, Ukraine.

show abstract

“…where A is the same linear continuous operator as in (2). The statement below is the main result of the present paper.…”

Section: Object Of Investigation and Main Resultsmentioning

confidence: 89%

Section: Object Of Investigation and Main Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Conditions for the existence of bounded solutions of nonlinear differential and functional differential equations

Slyusarchuk

2010

Ukr Math J

View full text Add to dashboard Cite

show abstract

“…The notions of c-continuous operators (in terms of ε and δ ) and c-completely continuous operators were introduced by Mukhamadiev [8,9]. These operators were studied in [9 -16].…”

Section: -Continuous and C -Completely Continuousmentioning

confidence: 99%

Method of local linear approximation in the theory of bounded solutions of nonlinear differential equations

Slyusarchuk

2009

Ukr Math J

View full text Add to dashboard Cite

517.988.6 The conditions for the existence of solutions of nonlinear differential equations in a space of functions bounded on the axis are established by using local linear approximations of these equations. Main Object of InvestigationLet E be a finite-dimensional Banach space with norm ⋅ E , let X and Y be arbitrary Banach spaces, and let L X Y ( , ) be a Banach space of linear continuous operators A acting from the space,We now consider differential operators F and G acting from the space C 1 (R , E) into the spaceR and defined by the formulaswhere the mappings f : R × E → E and g : E → E are continuous and, for any number r > 0,In view of the requirements imposed on the mappings f and g, the operators F and G are bounded. Recall that the operator C : X → Y is bounded if it maps every bounded set into a bounded set [1].

show abstract

“…Напомним, что понятия c-непрерывного оператора (на языке ε, δ) и c-вполне непрерывного оператора введены Э. Мухамадиевым (см. [5], [6]). Изучение этих понятий было продолжено в [7]- [12] и других работах.…”

unclassified

Ограниченные И Периодические Решения Нелинейных Дифференциально-Функциональных Уравнений

Слюсарчук¹,

Slyusarchuk²

2012

Матем. сб.

View full text Add to dashboard Cite

МАТЕМАТИЧЕСКИЙ СБОРНИКТом 203, № 5 УДК 517.988.6 В. Е. СлюсарчукОграниченные и периодические решения нелинейных дифференциально-функциональных уравненийПриведены условия существования ограниченных и периодических ре-шений нелинейного дифференциально-функционального уравненияиспользующие локальные линейные аппроксимации оператора F . Библиография: 23 названия.Ключевые слова: ограниченные и периодические решения, нелиней-ные дифференциально-функциональные уравнения, обратимость нели-нейных операторов.

show abstract

Investigations in the theory of bounded and periodic solutions of differential equations

Cited by 18 publications

References 0 publications

Conditions for the existence of bounded solutions of nonlinear differential and functional differential equations

Conditions for the existence of bounded solutions of nonlinear differential and functional differential equations

Method of local linear approximation in the theory of bounded solutions of nonlinear differential equations

Ограниченные И Периодические Решения Нелинейных Дифференциально-Функциональных Уравнений

Contact Info

Product

Resources

About