On weak solutions of functional-differential abstract nonlocal Cauchy problems

Ludwik Byszewski

Annales Polonici Mathematici (1997)

  • Volume: 65, Issue: 2, page 163-170
  • ISSN: 0066-2216

Abstract

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The existence, uniqueness and asymptotic stability of weak solutions of functional-differential abstract nonlocal Cauchy problems in a Banach space are studied. Methods of m-accretive operators and the Banach contraction theorem are applied.

How to cite

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Ludwik Byszewski. "On weak solutions of functional-differential abstract nonlocal Cauchy problems." Annales Polonici Mathematici 65.2 (1997): 163-170. <http://eudml.org/doc/269998>.

@article{LudwikByszewski1997,
abstract = {The existence, uniqueness and asymptotic stability of weak solutions of functional-differential abstract nonlocal Cauchy problems in a Banach space are studied. Methods of m-accretive operators and the Banach contraction theorem are applied.},
author = {Ludwik Byszewski},
journal = {Annales Polonici Mathematici},
keywords = {abstract Cauchy problems; functional-differential equation; nonlocal conditions; weak solutions; existence; uniqueness; asympto tic stability; m-accretive operators; Banach contraction theorem; asymptotic stability; functional-differential abstract nonlocal Cauchy problems in a Banach space; -accretive operators},
language = {eng},
number = {2},
pages = {163-170},
title = {On weak solutions of functional-differential abstract nonlocal Cauchy problems},
url = {http://eudml.org/doc/269998},
volume = {65},
year = {1997},
}

TY - JOUR
AU - Ludwik Byszewski
TI - On weak solutions of functional-differential abstract nonlocal Cauchy problems
JO - Annales Polonici Mathematici
PY - 1997
VL - 65
IS - 2
SP - 163
EP - 170
AB - The existence, uniqueness and asymptotic stability of weak solutions of functional-differential abstract nonlocal Cauchy problems in a Banach space are studied. Methods of m-accretive operators and the Banach contraction theorem are applied.
LA - eng
KW - abstract Cauchy problems; functional-differential equation; nonlocal conditions; weak solutions; existence; uniqueness; asympto tic stability; m-accretive operators; Banach contraction theorem; asymptotic stability; functional-differential abstract nonlocal Cauchy problems in a Banach space; -accretive operators
UR - http://eudml.org/doc/269998
ER -

References

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  4. [4] L. Byszewski, Existence and uniqueness of mild and classical solutions of semilinear functional-differential evolution nonlocal Cauchy problem, in: Selected Problems of Mathematics, Cracow University of Technology, Anniversary Issue 6 (1995), 25-33. 
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  7. [7] A. Kartsatos, A direct method for the existence of evolution operators associated with functional evolutions in general Banach spaces, Funkcial. Ekvac. 31 (1988), 89-102. Zbl0654.47028
  8. [8] A. Kartsatos and M. Parrott, A simplified approach to the existence and stability problem of a functional evolution equation in a general Banach space, in: Infinite Dimensional Systems, (F. Kappel and W. Schappacher (eds.), Lecture Notes in Math. 1076, Springer, Berlin, 1984, 115-122. Zbl0544.34064
  9. [9] T. Winiarska, Parabolic equations with coefficients depending on t and parameters, Ann. Polon. Math. 51 (1990), 325-339. Zbl0738.35020
  10. [10] T. Winiarska, Regularity of solutions of parabolic equations with coefficients depending on t and parameters, Ann. Polon. Math. 56 (1992), 311-317. Zbl0763.35015

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