Non-compact perturbations of m -accretive operators in general Banach spaces

Mieczysław Cichoń

Commentationes Mathematicae Universitatis Carolinae (1992)

  • Volume: 33, Issue: 3, page 403-409
  • ISSN: 0010-2628

Abstract

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In this paper we deal with the Cauchy problem for differential inclusions governed by m -accretive operators in general Banach spaces. We are interested in finding the sufficient conditions for the existence of integral solutions of the problem x ' ( t ) ∈ - A x ( t ) + f ( t , x ( t ) ) , x ( 0 ) = x 0 , where A is an m -accretive operator, and f is a continuous, but non-compact perturbation, satisfying some additional conditions.

How to cite

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Cichoń, Mieczysław. "Non-compact perturbations of $m$-accretive operators in general Banach spaces." Commentationes Mathematicae Universitatis Carolinae 33.3 (1992): 403-409. <http://eudml.org/doc/247390>.

@article{Cichoń1992,
abstract = {In this paper we deal with the Cauchy problem for differential inclusions governed by $m$-accretive operators in general Banach spaces. We are interested in finding the sufficient conditions for the existence of integral solutions of the problem $x^\{\prime \}(t)\in -A x(t)+f(t,x(t))$, $x(0)=x_0$, where $A$ is an $m$-accretive operator, and $f$ is a continuous, but non-compact perturbation, satisfying some additional conditions.},
author = {Cichoń, Mieczysław},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$m$-accretive operators; measures of noncompactness; differential inclusions; semigroups of contractions; nonlinear evolution equations; -accretive operator; equicontinuous semigroup},
language = {eng},
number = {3},
pages = {403-409},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Non-compact perturbations of $m$-accretive operators in general Banach spaces},
url = {http://eudml.org/doc/247390},
volume = {33},
year = {1992},
}

TY - JOUR
AU - Cichoń, Mieczysław
TI - Non-compact perturbations of $m$-accretive operators in general Banach spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1992
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 33
IS - 3
SP - 403
EP - 409
AB - In this paper we deal with the Cauchy problem for differential inclusions governed by $m$-accretive operators in general Banach spaces. We are interested in finding the sufficient conditions for the existence of integral solutions of the problem $x^{\prime }(t)\in -A x(t)+f(t,x(t))$, $x(0)=x_0$, where $A$ is an $m$-accretive operator, and $f$ is a continuous, but non-compact perturbation, satisfying some additional conditions.
LA - eng
KW - $m$-accretive operators; measures of noncompactness; differential inclusions; semigroups of contractions; nonlinear evolution equations; -accretive operator; equicontinuous semigroup
UR - http://eudml.org/doc/247390
ER -

References

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  2. Barbu V., Nonlinear Semigroups and Differential Equations in Banach Spaces, Noordhoff, Leyden, 1976. Zbl0328.47035MR0390843
  3. Cellina A., Marchi V., Non-convex perturbations of maximal monotone differential inclusions, Israel J. Math. 46 (1983), 1-11. (1983) Zbl0542.47036MR0727019
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  5. Colombo G., Fonda A., Ornelas A., Lower semicontinuous perturbations of maximal monotone differential inclusions, Israel J. Math. 61 (1988), 211-218. (1988) Zbl0661.47038MR0941237
  6. Daneš J., Generalized concentrative mappings and their fixed points, Comment. Math. Univ. Carolinae 11 (1970), 115-136. (1970) MR0263063
  7. Goncharov V.V., Tolstonogov A.A., Mutual continuous selections of multifunctions with non-convex values and its applications, Math. Sb. 182 (1991), 946-969. (1991) MR1128253
  8. Gutman S., Evolutions governed by m -accretive plus compact operators, Nonlinear Anal. Th. Math. Appl. 7 (1983), 707-717. (1983) Zbl0518.34055MR0707079
  9. Gutman S., Existence theorems for nonlinear evolution equations, ibid. 11 (1987), 1193-1206. (1987) Zbl0642.47055MR0913678
  10. Martin R.H., Jr., Nonlinear Operators and Differential Equations in Banach Spaces, John Wiley, New York-London-Sydney-Toronto, 1976. Zbl0333.47023MR0492671
  11. Mitidieri E., Vrabie I.I., Differential inclusions governed by non convex perturbations of m -accretive operators, Differential Integral Equations 2 (1989), 525-531. (1989) Zbl0736.34014MR0996758
  12. Schechter E., Evolution generated by semilinear dissipative plus compact operators, Trans. Amer. Math. Soc. 275 (1983), 297-308. (1983) Zbl0516.34061MR0678351
  13. Vrabie I.I., Compactness Methods for Nonlinear Evolutions, Pitman Monographs and Surveys in Pure and Applied Mathematics 32, Longman, Boston-London-Melbourne, 1987. Zbl0842.47040MR0932730

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