Startseite Optimal conditions of solvability of periodic problem for systems of differential equations with argument deviation
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Optimal conditions of solvability of periodic problem for systems of differential equations with argument deviation

  • Sulkhan Mukhigulashvili EMAIL logo
Veröffentlicht/Copyright: 30. September 2022
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Georgian Mathematical Journal
Aus der Zeitschrift Georgian Mathematical Journal Band 30 Heft 1

Abstract

In this paper, we study, on the interval I = [ a , b ] , the problem of the solvability and unique solvability of systems of higher-order differential equations with argument deviation

u i ( m i ) ( t ) = p i ( t ) u i + 1 ( τ i ( t ) ) + q i ( t )   ( i = 1 , … , n )

and

u i ( m i ) ( t ) = f i ( t , u i + 1 ( τ i ( t ) ) ) + q 0 ⁢ i ( t )   ( i = 1 , … , n ) ,

under the periodic boundary conditions

u i ( j ) ( b ) - u i ( j ) ( a ) = c i ⁢ j   ( i = 1 , … , n , j = 0 , … , m i - 1 ) ,

where u n + 1 = u 1 , n ≥ 2 , m i ≥ 1 , p i ∈ L ∞ ⁢ ( I ; R ) , q 0 ⁢ i ∈ L ⁢ ( I ; R ) , f i : I × R → R are Carathéodory class functions, and τ i : I → I are measurable functions. The optimal conditions are obtained, which guarantee the unique solvability of the linear problem and take into account the effect of argument deviation. Based on these results, the optimal conditions of the solvability and unique solvability are proved for the nonlinear problem.

Keywords: Higher-order system; periodic problem; argument deviations; unique solvability
MSC 2010: 34K13; 34B05

Funding statement: The research was supported by Grant FP-S-20-6376 of the Internal Grant Agency at Brno University of Technology.

References

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Received: 2021-11-30
Accepted: 2022-06-07
Published Online: 2022-09-30
Published in Print: 2023-02-01

© 2022 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Frontmatter
  2. On the well-posedness of nonlocal boundary value problems for a class of systems of linear generalized differential equations with singularities
  3. Products of Toeplitz operators with angular symbols
  4. Characterization of Lie-type higher derivations of triangular rings
  5. On classifying map of the integral Krichever–Hoehn formal group law
  6. Demicompactness perturbation in Banach algebras and some stability results
  7. On bicomplex 𝔹ℂ-modules lp 𝕜(𝔹ℂ) and some of their geometric properties
  8. On a class of nonlinear degenerate elliptic equations in weighted Sobolev spaces
  9. Asymptotic behaviors of solutions of a class of time-varying differential equations
  10. Fekete–Szegő problem of strongly α-close-to-convex functions associated with generalized fractional operator
  11. Some properties of Vitali sets
  12. Optimal conditions of solvability of periodic problem for systems of differential equations with argument deviation
  13. Generalized derivations with Engel condition on Lie ideals of prime rings
  14. Attractivity of implicit differential equations with composite fractional derivative
  15. Exponentially fitted difference scheme for singularly perturbed mixed integro-differential equations
https://doi.org/10.1515/gmj-2022-2182
Schlagwörter für diesen Artikel
Higher-order system; periodic problem; argument deviations; unique solvability

Artikel in diesem Heft

  1. Frontmatter
  2. On the well-posedness of nonlocal boundary value problems for a class of systems of linear generalized differential equations with singularities
  3. Products of Toeplitz operators with angular symbols
  4. Characterization of Lie-type higher derivations of triangular rings
  5. On classifying map of the integral Krichever–Hoehn formal group law
  6. Demicompactness perturbation in Banach algebras and some stability results
  7. On bicomplex 𝔹ℂ-modules lp 𝕜(𝔹ℂ) and some of their geometric properties
  8. On a class of nonlinear degenerate elliptic equations in weighted Sobolev spaces
  9. Asymptotic behaviors of solutions of a class of time-varying differential equations
  10. Fekete–Szegő problem of strongly α-close-to-convex functions associated with generalized fractional operator
  11. Some properties of Vitali sets
  12. Optimal conditions of solvability of periodic problem for systems of differential equations with argument deviation
  13. Generalized derivations with Engel condition on Lie ideals of prime rings
  14. Attractivity of implicit differential equations with composite fractional derivative
  15. Exponentially fitted difference scheme for singularly perturbed mixed integro-differential equations
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