Functional-differential equations with Riemann-Liouville integrals in the nonlinearities

Milan Medveď

Mathematica Bohemica (2014)

  • Volume: 139, Issue: 4, page 587-595
  • ISSN: 0862-7959

Abstract

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A sufficient condition for the nonexistence of blowing-up solutions to evolution functional-differential equations in Banach spaces with the Riemann-Liouville integrals in their right-hand sides is proved. The linear part of such type of equations is an infinitesimal generator of a strongly continuous semigroup of linear bounded operators. The proof of the main result is based on a desingularization method applied by the author in his papers on integral inequalities with weakly singular kernels. The result is illustrated on an example of a scalar equation with one Riemann-Liouville integral.

How to cite

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Medveď, Milan. "Functional-differential equations with Riemann-Liouville integrals in the nonlinearities." Mathematica Bohemica 139.4 (2014): 587-595. <http://eudml.org/doc/269866>.

@article{Medveď2014,
abstract = {A sufficient condition for the nonexistence of blowing-up solutions to evolution functional-differential equations in Banach spaces with the Riemann-Liouville integrals in their right-hand sides is proved. The linear part of such type of equations is an infinitesimal generator of a strongly continuous semigroup of linear bounded operators. The proof of the main result is based on a desingularization method applied by the author in his papers on integral inequalities with weakly singular kernels. The result is illustrated on an example of a scalar equation with one Riemann-Liouville integral.},
author = {Medveď, Milan},
journal = {Mathematica Bohemica},
keywords = {fractional differential equation; Riemann-Liouville integral; blowing-up solution; fractional differential equation; Riemann-Liouville integral; blowing-up solution},
language = {eng},
number = {4},
pages = {587-595},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Functional-differential equations with Riemann-Liouville integrals in the nonlinearities},
url = {http://eudml.org/doc/269866},
volume = {139},
year = {2014},
}

TY - JOUR
AU - Medveď, Milan
TI - Functional-differential equations with Riemann-Liouville integrals in the nonlinearities
JO - Mathematica Bohemica
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 139
IS - 4
SP - 587
EP - 595
AB - A sufficient condition for the nonexistence of blowing-up solutions to evolution functional-differential equations in Banach spaces with the Riemann-Liouville integrals in their right-hand sides is proved. The linear part of such type of equations is an infinitesimal generator of a strongly continuous semigroup of linear bounded operators. The proof of the main result is based on a desingularization method applied by the author in his papers on integral inequalities with weakly singular kernels. The result is illustrated on an example of a scalar equation with one Riemann-Liouville integral.
LA - eng
KW - fractional differential equation; Riemann-Liouville integral; blowing-up solution; fractional differential equation; Riemann-Liouville integral; blowing-up solution
UR - http://eudml.org/doc/269866
ER -

References

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