On positive periodic solutions of linear second order functional differential equations

Bravyi, Eugene

doi:10.1515/gmj-2016-0069

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2020

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“…Other interesting results about problems (6), (4) can be found also in the papers [10][11][12][13][14][15].…”

Section: Definition 12mentioning

confidence: 91%

Lasota–Opial type conditions for periodic problem for systems of higher-order functional differential equations

Mukhigulashvili

Půža

2020

J Inequal Appl

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In the paper we study the question of solvability and unique solvability of systems of the higher-order functional differential equations u (m i) i (t) = i (u i+1)(t) + q i (t) (i = 1, n) for t ∈ I := [a, b] and u (m i) i (t) = F i (u)(t) + q 0i (t) (i = 1, n) for t ∈ I under the periodic boundary conditions u (j) i (b)-u (j) i (a) = c ij (i = 1, n, j = 0, m i-1), where u n+1 = u 1 , m i ≥ 1, n ≥ 2, c ij ∈ R, q i , q 0i ∈ L(I; R), i : C 0 1 (I; R) → L(I; R) are monotone operators and F i are the local Caratheodory's class operators. In the paper in some sense optimal conditions that guarantee the unique solvability of the linear problem are obtained, and on the basis of these results the optimal conditions of the solvability and unique solvability for the nonlinear problem are proved.

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“…Other interesting results about problems (6), (4) can be found also in the papers [10][11][12][13][14][15].…”

Section: Definition 12mentioning

confidence: 91%

Lasota–Opial type conditions for periodic problem for systems of higher-order functional differential equations

Mukhigulashvili

Půža

2020

J Inequal Appl

View full text Add to dashboard Cite

show abstract

On positive periodic solutions of linear second order functional differential equations

Abstract: The periodic boundary value problem for linear second order functional differential equations is considered. Sharp sufficient conditions for the positiveness of solutions are obtained.

Cited by 1 publication

References 24 publications

Lasota–Opial type conditions for periodic problem for systems of higher-order functional differential equations

Lasota–Opial type conditions for periodic problem for systems of higher-order functional differential equations

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