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Weak solutions of first-order differential inclusions in Banach space

Year 2016, , 1 - 11, 17.12.2016
https://doi.org/10.30931/jetas.281375

Abstract

The aim of this paper is to investigate the existence of pseudo-solutions for a First- order
multivalued differential equation with nonlocal integral boundary condition in a Banach space.
Our approach is based on the use of the technique of measures of weak noncompactness and a fixed
point theorem of Mönch type.

References

  • [1] G. Adomian and G. E. Adomian, Cellular systems and aging models, Comput. Math. App. 11 (1985) 283-291.
  • [2] A. Arara and M. Benchohra, Fuzzy solutions for boundary value problems with integralboundary conditions, Acta Math. Univ. Comenianae LXXV (2006) 119-126.
  • [3] O. Arino, S. Gautier, J. P. Penot, A Fixed Point Theorem For Sequentially Continuous Mappings With Application To Ordinary Differential Equations, Funkcialaj Ekvcioj, 27 (1984) 273-279.
  • [4] J. P. Aubin, A. Cellina, Differential inclusions, Springer, Berlin, 1984.
  • [5] M. Benchohra, S. Hamani, J. Henderson, Functional differential inclusions with integral boundary conditions, Electron. J. Qua. Theory Di er. Equ. 15 (2007) 13 pages.
  • [6] M. Benchohra, J. R. Graef , F. Z. Mostefai, Weak solutions for boundary value problems with nonlinear fractional differential inclusions, Nonlinear Dynamics and Systems Theory. 11, 3 (2011) 227-237.
  • [7] M. Benchohra, F. Z. Mostefai, Weak solutions for nonlinear fractional differential equations with integral boundary conditions in Banach space, Opuscula Mathematica, 32, 1 (2012) 31-40.
  • [8] K. W. Blayneh, Analysis of age structured host-parasitoid model, FAR; East. J. Dyn. Syst. 4 (2002) 125-145.
  • [9] K. Chichon, Differential inclusions and multivalued integrals, Differential Inclusions, Control and Optimization 33 (2013) 171-191.
  • [10] F. S. De Blasi, On the property of the unit sphere in a Banach space, Bull. Math. Soc. Sci. Math. Roumanie (N. S.) 21 (1977) 259-262.
  • [11] L. Gorniewicz, Topological Fixed Point Theory of Multivalued Mappings, 2nd Edition, Springer, Netherlands, 2006.
  • [12] Hind H. G. Hashem, Weak solutions of differential equations in Banach space, Journal of fractional calculus and applications, 1, 3 (2012) 1-9.
  • [13] R. W. Ibrahim, The existence of weak solutions for fractional integral inclusions involving Pettis integral, Journal of Scientific and Mathematical Research, (2008)1-8.
  • [14] G. Infante, Eigenvalues and positive solutions of ODEs involving integral boundary conditions, Discrete Contin. Dyn. Syst. (2005) 436-442.
  • [15] Wu Jianrong Xue Xiaoping Wu Congxin, Existence theorem for weak solutions of Random differential inclusions in Banach spaces, Advences in Mathematics, 30, 4 (2001) 359-366.
  • [16] S. K. Pandey, D. K. Singh, P. Kumar and M. Kumar, Existence of measurable selectors in Pettis integrable multi function, 5, 1 (2014) 79-83.
  • [17] B. J. Pettis, On integration in vector spaces, Trans. Amer. Maths. Soc. 44 (1938) 277- 304.
  • [18] I. I. Vrabie, Compactness methods for nonlinear evolutions, Longman, Harlow, 1987.
  • [19] K. Yosida, Functional Analysis, Springer-Verlag, Berlin Heidelberg, New York 1980.
Year 2016, , 1 - 11, 17.12.2016
https://doi.org/10.30931/jetas.281375

Abstract

References

  • [1] G. Adomian and G. E. Adomian, Cellular systems and aging models, Comput. Math. App. 11 (1985) 283-291.
  • [2] A. Arara and M. Benchohra, Fuzzy solutions for boundary value problems with integralboundary conditions, Acta Math. Univ. Comenianae LXXV (2006) 119-126.
  • [3] O. Arino, S. Gautier, J. P. Penot, A Fixed Point Theorem For Sequentially Continuous Mappings With Application To Ordinary Differential Equations, Funkcialaj Ekvcioj, 27 (1984) 273-279.
  • [4] J. P. Aubin, A. Cellina, Differential inclusions, Springer, Berlin, 1984.
  • [5] M. Benchohra, S. Hamani, J. Henderson, Functional differential inclusions with integral boundary conditions, Electron. J. Qua. Theory Di er. Equ. 15 (2007) 13 pages.
  • [6] M. Benchohra, J. R. Graef , F. Z. Mostefai, Weak solutions for boundary value problems with nonlinear fractional differential inclusions, Nonlinear Dynamics and Systems Theory. 11, 3 (2011) 227-237.
  • [7] M. Benchohra, F. Z. Mostefai, Weak solutions for nonlinear fractional differential equations with integral boundary conditions in Banach space, Opuscula Mathematica, 32, 1 (2012) 31-40.
  • [8] K. W. Blayneh, Analysis of age structured host-parasitoid model, FAR; East. J. Dyn. Syst. 4 (2002) 125-145.
  • [9] K. Chichon, Differential inclusions and multivalued integrals, Differential Inclusions, Control and Optimization 33 (2013) 171-191.
  • [10] F. S. De Blasi, On the property of the unit sphere in a Banach space, Bull. Math. Soc. Sci. Math. Roumanie (N. S.) 21 (1977) 259-262.
  • [11] L. Gorniewicz, Topological Fixed Point Theory of Multivalued Mappings, 2nd Edition, Springer, Netherlands, 2006.
  • [12] Hind H. G. Hashem, Weak solutions of differential equations in Banach space, Journal of fractional calculus and applications, 1, 3 (2012) 1-9.
  • [13] R. W. Ibrahim, The existence of weak solutions for fractional integral inclusions involving Pettis integral, Journal of Scientific and Mathematical Research, (2008)1-8.
  • [14] G. Infante, Eigenvalues and positive solutions of ODEs involving integral boundary conditions, Discrete Contin. Dyn. Syst. (2005) 436-442.
  • [15] Wu Jianrong Xue Xiaoping Wu Congxin, Existence theorem for weak solutions of Random differential inclusions in Banach spaces, Advences in Mathematics, 30, 4 (2001) 359-366.
  • [16] S. K. Pandey, D. K. Singh, P. Kumar and M. Kumar, Existence of measurable selectors in Pettis integrable multi function, 5, 1 (2014) 79-83.
  • [17] B. J. Pettis, On integration in vector spaces, Trans. Amer. Maths. Soc. 44 (1938) 277- 304.
  • [18] I. I. Vrabie, Compactness methods for nonlinear evolutions, Longman, Harlow, 1987.
  • [19] K. Yosida, Functional Analysis, Springer-Verlag, Berlin Heidelberg, New York 1980.
There are 19 citations in total.

Details

Subjects Mathematical Sciences, Engineering
Journal Section Research Article
Authors

Khouni Yassine This is me

Publication Date December 17, 2016
Published in Issue Year 2016

Cite

APA Yassine, K. (2016). Weak solutions of first-order differential inclusions in Banach space. Journal of Engineering Technology and Applied Sciences, 1(1), 1-11. https://doi.org/10.30931/jetas.281375
AMA Yassine K. Weak solutions of first-order differential inclusions in Banach space. JETAS. May 2016;1(1):1-11. doi:10.30931/jetas.281375
Chicago Yassine, Khouni. “Weak Solutions of First-Order Differential Inclusions in Banach Space”. Journal of Engineering Technology and Applied Sciences 1, no. 1 (May 2016): 1-11. https://doi.org/10.30931/jetas.281375.
EndNote Yassine K (May 1, 2016) Weak solutions of first-order differential inclusions in Banach space. Journal of Engineering Technology and Applied Sciences 1 1 1–11.
IEEE K. Yassine, “Weak solutions of first-order differential inclusions in Banach space”, JETAS, vol. 1, no. 1, pp. 1–11, 2016, doi: 10.30931/jetas.281375.
ISNAD Yassine, Khouni. “Weak Solutions of First-Order Differential Inclusions in Banach Space”. Journal of Engineering Technology and Applied Sciences 1/1 (May 2016), 1-11. https://doi.org/10.30931/jetas.281375.
JAMA Yassine K. Weak solutions of first-order differential inclusions in Banach space. JETAS. 2016;1:1–11.
MLA Yassine, Khouni. “Weak Solutions of First-Order Differential Inclusions in Banach Space”. Journal of Engineering Technology and Applied Sciences, vol. 1, no. 1, 2016, pp. 1-11, doi:10.30931/jetas.281375.
Vancouver Yassine K. Weak solutions of first-order differential inclusions in Banach space. JETAS. 2016;1(1):1-11.