Existence of solutions of perturbed O.D.E.'s in Banach spaces

Giovanni Emmanuele

Commentationes Mathematicae Universitatis Carolinae (1991)

  • Volume: 32, Issue: 3, page 463-470
  • ISSN: 0010-2628

Abstract

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We consider a perturbed Cauchy problem like the following (PCP) x ' = A ( t , x ) + B ( t , x ) x ( 0 ) = x 0 and we present two results showing that (PCP) has a solution. In some cases, our theorems are more general than the previous ones obtained by other authors (see [4], [8], [9], [11], [13], [17], [18]).

How to cite

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Emmanuele, Giovanni. "Existence of solutions of perturbed O.D.E.'s in Banach spaces." Commentationes Mathematicae Universitatis Carolinae 32.3 (1991): 463-470. <http://eudml.org/doc/247316>.

@article{Emmanuele1991,
abstract = {We consider a perturbed Cauchy problem like the following \[ \{\hbox\{\rm (PCP)\}\} \left\lbrace \begin\{array\}\{ll\}x^\{\prime \} = A(t,x) +B(t,x) \ x(0)=x\_0 \end\{array\}\right.\] and we present two results showing that (PCP) has a solution. In some cases, our theorems are more general than the previous ones obtained by other authors (see [4], [8], [9], [11], [13], [17], [18]).},
author = {Emmanuele, Giovanni},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {perturbed Cauchy problem; semi-inner product; measure of noncompactness; ordinary differential equations; Banach space; local existence; Cauchy problem; measures of non-compactness},
language = {eng},
number = {3},
pages = {463-470},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Existence of solutions of perturbed O.D.E.'s in Banach spaces},
url = {http://eudml.org/doc/247316},
volume = {32},
year = {1991},
}

TY - JOUR
AU - Emmanuele, Giovanni
TI - Existence of solutions of perturbed O.D.E.'s in Banach spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1991
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 32
IS - 3
SP - 463
EP - 470
AB - We consider a perturbed Cauchy problem like the following \[ {\hbox{\rm (PCP)}} \left\lbrace \begin{array}{ll}x^{\prime } = A(t,x) +B(t,x) \ x(0)=x_0 \end{array}\right.\] and we present two results showing that (PCP) has a solution. In some cases, our theorems are more general than the previous ones obtained by other authors (see [4], [8], [9], [11], [13], [17], [18]).
LA - eng
KW - perturbed Cauchy problem; semi-inner product; measure of noncompactness; ordinary differential equations; Banach space; local existence; Cauchy problem; measures of non-compactness
UR - http://eudml.org/doc/247316
ER -

References

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  9. Emmanuele G., Existence of approximate solutions for O.D.E.'s under Carathéodory assumptions in closed, convex sets of Banach spaces, Funkcialaj Ekvacioj, to appear. 
  10. Evans L.C., Nonlinear evolution equations in an arbitrary Banach space, Israel J. Math. 26 (1977), 1-42. (1977) Zbl0349.34043MR0440431
  11. Hu Shou Chuan, Ordinary differential equations involving perturbations in Banach spaces, J. Nonlinear Analysis, TMA 7 (1983), 933-940. (1983) MR0713206
  12. Kato T., Nonlinear semigroups and evolution equations, J. Math. Soc. Japan 19 (1967), 508-520. (1967) Zbl0163.38303MR0226230
  13. Martin R.H., Remarks on ordinary differential equations involving dissipative and compact operators, J. London Math. Soc. 10 (1975), 61-65. (1975) Zbl0305.34092MR0369849
  14. Martin R.H., Nonlinear operators and differential equations in Banach spaces, Wiley and Sons 1976. Zbl0333.47023MR0492671
  15. Pierre M., Enveloppe d'une famille de semi-groups dans un espace de Banach, C.R. Acad. Sci. Paris 284 (1977), 401-404. (1977) MR0440432
  16. Ricceri B., Villani A., Separability and Scorza-Dragoni's property, Le Matematiche 37 (1982), 156-161. (1982) MR0791334
  17. Schechter E., Evolution generated by continuous dissipative plus compact operators, Bull. London Math. Soc. 13 (1981), 303-308. (1981) Zbl0443.34061MR0620042
  18. Volkmann P., Ein Existenzsatz für gewöhnliche differentialgleichungen in Banachräumen, Proc. Amer. Math. Soc. 80 (1980), 297-300. (1980) Zbl0506.34051MR0577763

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