Trichotomy and bounded solutions of nonlinear differential equations

Mieczysław Cichoń

Mathematica Bohemica (1994)

  • Volume: 119, Issue: 3, page 275-284
  • ISSN: 0862-7959

Abstract

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The existence of bounded solutions for equations x ' = A ( t ) x + f ( t , x ) in Banach spaces is proved. We assume that the linear part is trichotomic and the perturbation f satisfies some conditions expressed in terms of measures of noncompactness.

How to cite

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Cichoń, Mieczysław. "Trichotomy and bounded solutions of nonlinear differential equations." Mathematica Bohemica 119.3 (1994): 275-284. <http://eudml.org/doc/29315>.

@article{Cichoń1994,
abstract = {The existence of bounded solutions for equations $x^\{\prime \}=A(t)x+f(t,x)$ in Banach spaces is proved. We assume that the linear part is trichotomic and the perturbation $f$ satisfies some conditions expressed in terms of measures of noncompactness.},
author = {Cichoń, Mieczysław},
journal = {Mathematica Bohemica},
keywords = {existence; bounded solutions; quasilinear differential; trichotomy; measures of noncompactness; Banach spaces; existence; bounded solutions; quasilinear differential},
language = {eng},
number = {3},
pages = {275-284},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Trichotomy and bounded solutions of nonlinear differential equations},
url = {http://eudml.org/doc/29315},
volume = {119},
year = {1994},
}

TY - JOUR
AU - Cichoń, Mieczysław
TI - Trichotomy and bounded solutions of nonlinear differential equations
JO - Mathematica Bohemica
PY - 1994
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 119
IS - 3
SP - 275
EP - 284
AB - The existence of bounded solutions for equations $x^{\prime }=A(t)x+f(t,x)$ in Banach spaces is proved. We assume that the linear part is trichotomic and the perturbation $f$ satisfies some conditions expressed in terms of measures of noncompactness.
LA - eng
KW - existence; bounded solutions; quasilinear differential; trichotomy; measures of noncompactness; Banach spaces; existence; bounded solutions; quasilinear differential
UR - http://eudml.org/doc/29315
ER -

References

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  3. M. Cichoń, A point of view on measures of noncompactness, Demonstr. Math. 26 (1993). in press. (1993) MR1265840
  4. J. L. Daleckii, M. G. Krein, Stability of Solutions of Ordinary Differential Equations in Banach Spaces, Moscow, 1970. (In Russian.) (1970) 
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  7. S. Elaydi, O. Hajek, Exponential dichotomy and trichotomy of nonlinear differential equations, Diff. Integral Equations 3 (1990), 1201-1204. (1990) Zbl0722.34053MR1073067
  8. D. L. Lovelady, Bounded solutions of whole-line differential equations, Bull. AMS 79 (1972), 752-753. (1972) MR0322267
  9. J. L. Massera, J. J. Schäffer, Linear Differential Equations and Function Spaces, New York-London, 1966. (1966) MR0212324
  10. P. Preda, M. Megan, Exponential dichotomy of evolutionary processes in Banach spaces, Czechoslovak Math. Јour. 35 (1985), 312-323. (1985) Zbl0609.47051MR0787133
  11. B. Przeradzki, 10.4064/ap-56-2-103-121, Ann. Polon. Math. 56 (1992), 103-121. (1992) Zbl0805.47041MR1159982DOI10.4064/ap-56-2-103-121
  12. B. N. Sadovskii, A fixed point principle, Functional Analysis and its Applications 1 (1967), 151-153. (In Russian.) (1967) MR0211302
  13. S. Szufla, On the existence of bounded solutions of nonlinear differential equations in Banach spaces, Funct. Approx. 15 (1986), 117-123. (1986) Zbl0617.34061MR0880140

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