Existence of extremal solutions and comparison results for delay differential equations in abstract cones

A. S. Vatsala; R. L. Vaughn

Rendiconti del Seminario Matematico della Università di Padova (1981)

  • Volume: 64, page 1-14
  • ISSN: 0041-8994

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Vatsala, A. S., and Vaughn, R. L.. "Existence of extremal solutions and comparison results for delay differential equations in abstract cones." Rendiconti del Seminario Matematico della Università di Padova 64 (1981): 1-14. <http://eudml.org/doc/107794>.

@article{Vatsala1981,
author = {Vatsala, A. S., Vaughn, R. L.},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {extremal solutions; Cauchy problem; comparison theorems; Banach space},
language = {eng},
pages = {1-14},
publisher = {Seminario Matematico of the University of Padua},
title = {Existence of extremal solutions and comparison results for delay differential equations in abstract cones},
url = {http://eudml.org/doc/107794},
volume = {64},
year = {1981},
}

TY - JOUR
AU - Vatsala, A. S.
AU - Vaughn, R. L.
TI - Existence of extremal solutions and comparison results for delay differential equations in abstract cones
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1981
PB - Seminario Matematico of the University of Padua
VL - 64
SP - 1
EP - 14
LA - eng
KW - extremal solutions; Cauchy problem; comparison theorems; Banach space
UR - http://eudml.org/doc/107794
ER -

References

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  1. [1] Darbo, Punti uniti in trasformazioni a codominio noncompatto, Rend. Sem. Mat. Univ. Padova, 24 (1955), pp. 84-92. Zbl0064.35704MR70164
  2. [2] K. Deimling, Ordinary Differential Equations in Banach Spaces, Lect. Notes, Vol. 596, Springer-Verlag (1977). Zbl0361.34050MR463601
  3. [3] K. Kurtowski, Topology, Vol. II, Academic Press, New York (1966). MR217751
  4. [4] V. Lakshmikantham - S. Leela, An introduction to nonlinear differential equations in abstract spaces, Pergamon Press (1980). Zbl0456.34002MR616449
  5. [5] V. Lakshmikantham, Comparison results for reaction-diffusion equations in Banach space, Lecture notes of talks delivered at the conference on « A survey of theoretical and numerical trends in nonlinear analysis » at Bari, Italy. Zbl0433.35035
  6. [6] V. Lakshmikantham - A.R. Mitchell - R.W. Mitchell, On the existence of solutions of differential equations of retarded type in a Banach space, Annals Polonic Mathematics, 35 (1978), pp. 253-260. Zbl0373.34034MR477377
  7. [7] V. Lakshmikantham - A.R. Mitchell - R.W. Mitchell, Maximal and minimal solutions and comparison results for differential equations in abstract cones, Annals Polonic Mathematics, 38 (1977), pp. 317-324. Zbl0367.34047MR597533
  8. [8] V. Lakshmikantham - V. Leela - V. Mouro, Existence and uniqueness of solutions of delay differential equations on a closed subset of a Banach space, Nonlinear Analysis, Vol. 2, No. 3, 311-327. Zbl0384.34040MR512662
  9. [9] S. Leela - V. Mouro, Existence of solutions in a closed set for delay differential equations in Banach spaces, Nonlinear Analysis, Vol. 2 (1978), pp. 47-85. Zbl0383.34053MR512653
  10. [10] R.H. Martin, Non linear operators and differential equations in a Banach space, John Wiley and Sons, New York (1976). 
  11. [11] V. Lakshmikantham - S. Leela, Differential and integral inequalities, Vol. I and II, Academic Press (1968). Zbl0177.12403

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