BibTex RIS Kaynak Göster

BOUNDEDLY SOLVABILITY OF FIRST ORDER DELAY DIFFERENTIAL OPERATORS WITH PIECEWISE CONSTANT ARGUMENTS

Yıl 2019, Cilt: 9 Sayı: 2, 396 - 403, 01.06.2019

Öz

Using the methods of operator theory, we investigate all boundedly solvable extensions of a minimal operator generated by rst order delay di erential-operator expression with piecewise constant argument in the Hilbert space of vector-functions at nite interval. Also spectrum of these extensions is studied.

Kaynakça

  • [1] Bereketoglu H., Seyhan Oztepe G. and Ogun A., (2010), Advanced impulsive differential equations with piecewise constant arguments, Mathematical Modelling and Analysis, 15, 2, pp. 175-187.
  • [2] Bereketoglu H., Lafcı M. and Seyhan Oztepe G., (2017), Qualitative properties of a third-order differential equation with a piecewise constant argument, Electronic Journal of Differential Equations, 93, pp. 1-12.
  • [3] Bereketoglu H., Lafcı M. and Seyhan Oztepe G., (2017), On the oscillation of a third order nonlinear differential equation with piecewise constant argument, Mediterr. J. Math., 14, 3, Art. 123, 19 pp.
  • [4] Cabada A. and Ferreiro J. B., (2011), First order differential equations with piecewise constant arguments and nonlinear boundary value conditions, Journal of Mathematical Analysis and Applications, 380, pp. 124-136.
  • [5] Cooke, K. L. and Wiener J., (1984), Retarded differential equations with piecewise constant delays, Journal of Mathematical Analysis and Applications, 99, pp. 265-29
  • 6] Goldstein, J. A., (1985), Semigroups of Linear Operators and Applications, New York, Oxford University Press.
  • [7] Gorbachuk, V. I. and Gorbachuk, M. L., (1991), Boundary Value Problems for Operator Differential Equations, Dordrecht, Kluwer Academic Publisher.
  • [8] H¨ormander L., (1995), On the theory of general partial differential operators. Acta Mathematica, 94, pp. 161-248.
  • [9] Ismailov, Z. I. and Ipek, P., (2014), Spectrums of solvable pantograph differential-operators for first order, Abstract and Applied Analysis, 2014, pp. 1-8.
  • [10] Karakoc, F., Bereketoglu, H. and Seyhan, G., (2010), Oscillatory and periodic solutions of impulsive differential equations with piecewise constant argument, Acta Appl. Math., 110, 1, pp. 499-510.
  • [11] Seyhan Oztepe G., (2017), Existence and qualitative properties of solutions of a second order mixed type impulsive differential equation with piecewise constant arguments, Hacettepe Journal of Mathematics and Statistics, 46, 6, pp. 1077-1091.
  • [12] Seyhan Oztepe G., Karakoc, F. and Bereketoglu, H., (2017), Oscillation and periodicity of a second order impulsive delay differential equation with a piecewise constant argument. Commun. Math. 25 , pp. 89-98
Yıl 2019, Cilt: 9 Sayı: 2, 396 - 403, 01.06.2019

Öz

Kaynakça

  • [1] Bereketoglu H., Seyhan Oztepe G. and Ogun A., (2010), Advanced impulsive differential equations with piecewise constant arguments, Mathematical Modelling and Analysis, 15, 2, pp. 175-187.
  • [2] Bereketoglu H., Lafcı M. and Seyhan Oztepe G., (2017), Qualitative properties of a third-order differential equation with a piecewise constant argument, Electronic Journal of Differential Equations, 93, pp. 1-12.
  • [3] Bereketoglu H., Lafcı M. and Seyhan Oztepe G., (2017), On the oscillation of a third order nonlinear differential equation with piecewise constant argument, Mediterr. J. Math., 14, 3, Art. 123, 19 pp.
  • [4] Cabada A. and Ferreiro J. B., (2011), First order differential equations with piecewise constant arguments and nonlinear boundary value conditions, Journal of Mathematical Analysis and Applications, 380, pp. 124-136.
  • [5] Cooke, K. L. and Wiener J., (1984), Retarded differential equations with piecewise constant delays, Journal of Mathematical Analysis and Applications, 99, pp. 265-29
  • 6] Goldstein, J. A., (1985), Semigroups of Linear Operators and Applications, New York, Oxford University Press.
  • [7] Gorbachuk, V. I. and Gorbachuk, M. L., (1991), Boundary Value Problems for Operator Differential Equations, Dordrecht, Kluwer Academic Publisher.
  • [8] H¨ormander L., (1995), On the theory of general partial differential operators. Acta Mathematica, 94, pp. 161-248.
  • [9] Ismailov, Z. I. and Ipek, P., (2014), Spectrums of solvable pantograph differential-operators for first order, Abstract and Applied Analysis, 2014, pp. 1-8.
  • [10] Karakoc, F., Bereketoglu, H. and Seyhan, G., (2010), Oscillatory and periodic solutions of impulsive differential equations with piecewise constant argument, Acta Appl. Math., 110, 1, pp. 499-510.
  • [11] Seyhan Oztepe G., (2017), Existence and qualitative properties of solutions of a second order mixed type impulsive differential equation with piecewise constant arguments, Hacettepe Journal of Mathematics and Statistics, 46, 6, pp. 1077-1091.
  • [12] Seyhan Oztepe G., Karakoc, F. and Bereketoglu, H., (2017), Oscillation and periodicity of a second order impulsive delay differential equation with a piecewise constant argument. Commun. Math. 25 , pp. 89-98
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

P. Ipek Al Bu kişi benim

Z. I. Ismailov Bu kişi benim

Yayımlanma Tarihi 1 Haziran 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 9 Sayı: 2

Kaynak Göster