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Yıl 2021, Cilt: 5 Sayı: 3, 433 - 444, 30.09.2021
https://doi.org/10.31197/atnaa.814109

Öz

Kaynakça

  • Hamdy M. Ahmed, Boundary controllability of impulsive nonlinear fractional delay integro-differential system, Cogent Engineering 3:1, DOI: 10.1080/23311916.2016.1215766.
  • H. Akca, V. Covachev and Z. Covacheva, Existence theorem for a second-order impulsive functional-differential equation with a nonlocal condition, J. Nonlinear Convex Anal. 17 (2016), no. 6, 1129–1136.
  • K. Balachandran and E.R. Anandhi, Boundary controllability of delay integrodifferential systems in Banach spaces, J. Korean Soc. Ind. Appl. Math. 4 (2000), no. 2, 67–75.
  • K. Balachandran and M. Chandrasekaran, Existence of solutions of delay differential equation with nonlocal condition, Indian J. Pure Appl. Math. 27 (1996), no. 5, 443– 449.
  • K. Balachandran and R.R. Kumar, Existence of solutions of integrodifferential evolution equations with time varying delays, Appl. Math. E-Notes 7 (2007), 1–8.
  • L. Byszewski, Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J. Math. Anal. Appl. 162 (1991), no. 1, 496–505.
  • X. Fu and X. Liu, Existence of solutions for neutral non-autonomous evolution equations with nonlocal conditions, Indian J. Pure Appl. Math. 37 (2006), no. 3, 179–192.
  • K. Kumar and R. Kumar, Controllability results for general integrodifferential evolution equations in Banach space, Differ. Uravn. Protsessy Upr. 2015 (2015), no. 3, 1–15.
  • D.G. Park, K. Balachandran and F.P. Samuel, Regularity of solutions of abstract quasilinear delay integrodifferential equations, J. Korean Math. Soc. 48 (2011), no. 3, 585–597.
  • A. Pazy, Semigroup of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983.
  • T. Winirska, Nonlinear evolution equation with parameter, Bull. Pol. Acad. Sci. Math. 37 (1989), 157–162.
  • S. Xie, Existence of solutions for nonlinear mixed type integro-differential functional evolution equations with nonlocal conditions, Bound. Value Probl. 2012 (2012), 100. https://doi.org/10.1186/1687-2770-2012-100.
  • Z. Yan, Existence for a nonlinear impulsive functional integrodifferential equation with nonlocal conditions in Banach spaces, J. Appl. Math. Inform. 29 (2011), no. 3-4, 681–696.

Nonlinear Integrodifferential Equations with Time Varying Delay

Yıl 2021, Cilt: 5 Sayı: 3, 433 - 444, 30.09.2021
https://doi.org/10.31197/atnaa.814109

Öz

By practicing the manner of semigroup theory and Banach contraction theorem, the existence and uniqueness of mild and classical solutions of nonlinear integrodifferential equations with time varying delay in Banach spaces is showed. Certainly, an example is revealed to justify the abstract idea.

By practicing the manner of semigroup theory and Banach contraction theorem, the existence and uniqueness of mild and classical solutions of nonlinear integrodifferential equations with time varying delay in Banach spaces is showed. Certainly, an example is revealed to justify the abstract idea.

Kaynakça

  • Hamdy M. Ahmed, Boundary controllability of impulsive nonlinear fractional delay integro-differential system, Cogent Engineering 3:1, DOI: 10.1080/23311916.2016.1215766.
  • H. Akca, V. Covachev and Z. Covacheva, Existence theorem for a second-order impulsive functional-differential equation with a nonlocal condition, J. Nonlinear Convex Anal. 17 (2016), no. 6, 1129–1136.
  • K. Balachandran and E.R. Anandhi, Boundary controllability of delay integrodifferential systems in Banach spaces, J. Korean Soc. Ind. Appl. Math. 4 (2000), no. 2, 67–75.
  • K. Balachandran and M. Chandrasekaran, Existence of solutions of delay differential equation with nonlocal condition, Indian J. Pure Appl. Math. 27 (1996), no. 5, 443– 449.
  • K. Balachandran and R.R. Kumar, Existence of solutions of integrodifferential evolution equations with time varying delays, Appl. Math. E-Notes 7 (2007), 1–8.
  • L. Byszewski, Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J. Math. Anal. Appl. 162 (1991), no. 1, 496–505.
  • X. Fu and X. Liu, Existence of solutions for neutral non-autonomous evolution equations with nonlocal conditions, Indian J. Pure Appl. Math. 37 (2006), no. 3, 179–192.
  • K. Kumar and R. Kumar, Controllability results for general integrodifferential evolution equations in Banach space, Differ. Uravn. Protsessy Upr. 2015 (2015), no. 3, 1–15.
  • D.G. Park, K. Balachandran and F.P. Samuel, Regularity of solutions of abstract quasilinear delay integrodifferential equations, J. Korean Math. Soc. 48 (2011), no. 3, 585–597.
  • A. Pazy, Semigroup of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983.
  • T. Winirska, Nonlinear evolution equation with parameter, Bull. Pol. Acad. Sci. Math. 37 (1989), 157–162.
  • S. Xie, Existence of solutions for nonlinear mixed type integro-differential functional evolution equations with nonlocal conditions, Bound. Value Probl. 2012 (2012), 100. https://doi.org/10.1186/1687-2770-2012-100.
  • Z. Yan, Existence for a nonlinear impulsive functional integrodifferential equation with nonlocal conditions in Banach spaces, J. Appl. Math. Inform. 29 (2011), no. 3-4, 681–696.
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Kamalendra Kumar Bu kişi benim 0000-0001-5490-4855

Manoj Karnatak Bu kişi benim 0000-0001-7707-6933

Rakesh Kumar 0000-0001-6399-2471

Yayımlanma Tarihi 30 Eylül 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 5 Sayı: 3

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