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Quasilinear Evolution Integrodifferential Equations in Banach Spaces

Yıl 2019, Sayı: 27, 11 - 21, 01.03.2019

Öz

Existence and uniqueness of local classical
solutions of the quasilinear evolution integrodifferential equation in Banach
spaces are studied. The results are demonstrated by employing the fixed point
technique on C_0-semigroup of bounded linear operator. At last, we
deal an example to interpret the theory.

Kaynakça

  • [1] S. Abbas and D. Bahuguna, Existence of solutions to a quasilinear functional differential equations, Electronic Journal of Differential Equations, Vol. 2009(2009), no. 164, pp. 1–8.
  • [2] H. Aman, Quasilinear evolution equations and parabolic systems, Transactions of the American mathematical society, 293 (1986), no.1, 191-227.
  • [3] E. H. Anderson, M. J. Anderson and W.T. England, Nonhomogeneous quasilinear evolution equations, Journal of integral equations, 3(1981), no.2, 175-184.
  • [4] D. Bahuguna, Quasilinear integrodifferential equations in Banach spaces, Nonlinear Analysis 24 (1995), 175-183.
  • [5] D. Bahuguna, Regularity solutions to quasilinear integrodifferential equations in Banach spaces, Appl. Anal. 62 (1996), 1-9.
  • [6] K. Balachandran and D.G. Park, Existence of solutions of quasilinear integrodifferential evolution equations in Banach spaces, Bull. Korean Math. Soc., 46(2009), no.4, 691-700.
  • [7] R. S. Dubey, Existence of a Regular solution to quasilinear implicit integrodifferential equations in Banach space, Nonlinear Dynamics and Systems Theory,11(2) (2011) 137–146.
  • [8] R. Haloi, D. Bahuguna and D. N. Pandey, Electronic Journal of Differential Equations, Vol. 2012 (2012), No no. 13, pp. 1–10.
  • [9] S. Kato, Nonhomogeneous quasilinear evolution equations in Banach spaces, Nonlinear Analysis,9(1985), 1061-1071.
  • [10] T. Kato, Quasilinear equations of evolution with application to partial differential equations, Lecture Notes in Math. 448(1975), 25-70.
  • [11] A. Pazy, Semigroup of Linear Operators and Applications to Partial Differential Equations, Springer Verlag, New York, 1983.
  • [12] F. P. Samuel and K. Balachandran, Existence of solutions of quasilinear integrodifferential evolution equations with impulsive conditions, Thai Journal of Mathematics, 9(2011), no.1, 139-152.
  • [13] F. P. Samuel, T.R. Lisso and K.Z. Kaunda, Existence solutions for quasilinear evolution integrodifferential equations with infinite delay, International Journal of Engineering and Technical Research (IJETR), 2(4), April 2014.
  • [14] N. Sanekata, Abstract quasilinear equations of evolution in nonreflexive Banach spaces, Hiroshima Mathematical Journal, 19(1989), 109-139.
  • [15] K. Yosida, Functional Analysis, springer (1968).
Yıl 2019, Sayı: 27, 11 - 21, 01.03.2019

Öz

Kaynakça

  • [1] S. Abbas and D. Bahuguna, Existence of solutions to a quasilinear functional differential equations, Electronic Journal of Differential Equations, Vol. 2009(2009), no. 164, pp. 1–8.
  • [2] H. Aman, Quasilinear evolution equations and parabolic systems, Transactions of the American mathematical society, 293 (1986), no.1, 191-227.
  • [3] E. H. Anderson, M. J. Anderson and W.T. England, Nonhomogeneous quasilinear evolution equations, Journal of integral equations, 3(1981), no.2, 175-184.
  • [4] D. Bahuguna, Quasilinear integrodifferential equations in Banach spaces, Nonlinear Analysis 24 (1995), 175-183.
  • [5] D. Bahuguna, Regularity solutions to quasilinear integrodifferential equations in Banach spaces, Appl. Anal. 62 (1996), 1-9.
  • [6] K. Balachandran and D.G. Park, Existence of solutions of quasilinear integrodifferential evolution equations in Banach spaces, Bull. Korean Math. Soc., 46(2009), no.4, 691-700.
  • [7] R. S. Dubey, Existence of a Regular solution to quasilinear implicit integrodifferential equations in Banach space, Nonlinear Dynamics and Systems Theory,11(2) (2011) 137–146.
  • [8] R. Haloi, D. Bahuguna and D. N. Pandey, Electronic Journal of Differential Equations, Vol. 2012 (2012), No no. 13, pp. 1–10.
  • [9] S. Kato, Nonhomogeneous quasilinear evolution equations in Banach spaces, Nonlinear Analysis,9(1985), 1061-1071.
  • [10] T. Kato, Quasilinear equations of evolution with application to partial differential equations, Lecture Notes in Math. 448(1975), 25-70.
  • [11] A. Pazy, Semigroup of Linear Operators and Applications to Partial Differential Equations, Springer Verlag, New York, 1983.
  • [12] F. P. Samuel and K. Balachandran, Existence of solutions of quasilinear integrodifferential evolution equations with impulsive conditions, Thai Journal of Mathematics, 9(2011), no.1, 139-152.
  • [13] F. P. Samuel, T.R. Lisso and K.Z. Kaunda, Existence solutions for quasilinear evolution integrodifferential equations with infinite delay, International Journal of Engineering and Technical Research (IJETR), 2(4), April 2014.
  • [14] N. Sanekata, Abstract quasilinear equations of evolution in nonreflexive Banach spaces, Hiroshima Mathematical Journal, 19(1989), 109-139.
  • [15] K. Yosida, Functional Analysis, springer (1968).
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Kamalendra Kumar Bu kişi benim

Rakesh Kumar

Manoj Karnatak Bu kişi benim

Yayımlanma Tarihi 1 Mart 2019
Gönderilme Tarihi 24 Ağustos 2018
Yayımlandığı Sayı Yıl 2019 Sayı: 27

Kaynak Göster

APA Kumar, K., Kumar, R., & Karnatak, M. (2019). Quasilinear Evolution Integrodifferential Equations in Banach Spaces. Journal of New Theory(27), 11-21.
AMA Kumar K, Kumar R, Karnatak M. Quasilinear Evolution Integrodifferential Equations in Banach Spaces. JNT. Mart 2019;(27):11-21.
Chicago Kumar, Kamalendra, Rakesh Kumar, ve Manoj Karnatak. “Quasilinear Evolution Integrodifferential Equations in Banach Spaces”. Journal of New Theory, sy. 27 (Mart 2019): 11-21.
EndNote Kumar K, Kumar R, Karnatak M (01 Mart 2019) Quasilinear Evolution Integrodifferential Equations in Banach Spaces. Journal of New Theory 27 11–21.
IEEE K. Kumar, R. Kumar, ve M. Karnatak, “Quasilinear Evolution Integrodifferential Equations in Banach Spaces”, JNT, sy. 27, ss. 11–21, Mart 2019.
ISNAD Kumar, Kamalendra vd. “Quasilinear Evolution Integrodifferential Equations in Banach Spaces”. Journal of New Theory 27 (Mart 2019), 11-21.
JAMA Kumar K, Kumar R, Karnatak M. Quasilinear Evolution Integrodifferential Equations in Banach Spaces. JNT. 2019;:11–21.
MLA Kumar, Kamalendra vd. “Quasilinear Evolution Integrodifferential Equations in Banach Spaces”. Journal of New Theory, sy. 27, 2019, ss. 11-21.
Vancouver Kumar K, Kumar R, Karnatak M. Quasilinear Evolution Integrodifferential Equations in Banach Spaces. JNT. 2019(27):11-2.


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