Existence of solutions for integrodifferential inclusions in Banach spaces

Nikolaos S. Papageorgiou

Commentationes Mathematicae Universitatis Carolinae (1991)

  • Volume: 32, Issue: 4, page 687-696
  • ISSN: 0010-2628

Abstract

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In this paper we examine nonlinear integrodifferential inclusions defined in a separable Banach space. Using a compactness type hypothesis involving the ball measure of noncompactness, we establish two existence results. One involving convex-valued orientor fields and the other nonconvex valued ones.

How to cite

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Papageorgiou, Nikolaos S.. "Existence of solutions for integrodifferential inclusions in Banach spaces." Commentationes Mathematicae Universitatis Carolinae 32.4 (1991): 687-696. <http://eudml.org/doc/21812>.

@article{Papageorgiou1991,
abstract = {In this paper we examine nonlinear integrodifferential inclusions defined in a separable Banach space. Using a compactness type hypothesis involving the ball measure of noncompactness, we establish two existence results. One involving convex-valued orientor fields and the other nonconvex valued ones.},
author = {Papageorgiou, Nikolaos S.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {sublinear measure of noncompactness; orientor; field; selector; upper semicontinuity; lower semicontinuity; graph measurability; weak measurability; existence; integrodifferential inclusion; Banach space; Volterra integral operator; measure of noncompactness},
language = {eng},
number = {4},
pages = {687-696},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Existence of solutions for integrodifferential inclusions in Banach spaces},
url = {http://eudml.org/doc/21812},
volume = {32},
year = {1991},
}

TY - JOUR
AU - Papageorgiou, Nikolaos S.
TI - Existence of solutions for integrodifferential inclusions in Banach spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1991
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 32
IS - 4
SP - 687
EP - 696
AB - In this paper we examine nonlinear integrodifferential inclusions defined in a separable Banach space. Using a compactness type hypothesis involving the ball measure of noncompactness, we establish two existence results. One involving convex-valued orientor fields and the other nonconvex valued ones.
LA - eng
KW - sublinear measure of noncompactness; orientor; field; selector; upper semicontinuity; lower semicontinuity; graph measurability; weak measurability; existence; integrodifferential inclusion; Banach space; Volterra integral operator; measure of noncompactness
UR - http://eudml.org/doc/21812
ER -

References

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  1. Banas J., Goebel K., Measures of Noncompactness in Banach Spaces, Marcel Dekker, New York, 1980. Zbl0441.47056MR0591679
  2. Bressan A., Colombo G., Extensions and selections of maps with decomposable values, Studia Math. 90 (1988), 69-86. (1988) Zbl0677.54013MR0947921
  3. Davy J.L., Properties of the solution set of a generalized differential equation, Bulletin of the Australian Math. Soc. 6 (1974), 379-398. (1974) MR0303023
  4. Kandilakis D., Papageorgiou N.S., On the properties of the Aumann integral with applications to differential inclusions and control systems, Czech. Math. Journ. 39 (1989), 1-15. (1989) Zbl0677.28005MR0983479
  5. Kisielewicz M., Multivalued differential equations in separable Banach spaces, Journ. of Optim. Theory Appl. 37 (1982), 231-249. (1982) Zbl0458.34008MR0663523
  6. Klein E., Thompson A., Theory of Correspondence, Wiley, New York, 1984. MR0752692
  7. Mönch H., Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces, Nonlin. Anal.-TMA 4 (1980), 985-999. (1980) MR0586861
  8. Mukshinov A., On differential inclusions in Banach spaces, Soviet Math. Doklady 15 (1976), 1122-1125. (1976) 
  9. Pachpatte B., A note on Gronwall-Bellman inequality, J. Math. Anal. Appl. 44 (1973), 758-762. (1973) Zbl0274.45011MR0335721
  10. Papageorgiou N.S., On the theory of Banach space valued multifunctions. Part 1: Integration and conditional expectation, J. Multiv. Anal. 17 (1985), 185-206. (1985) MR0808276
  11. Papageorgiou N.S., Convergence theorems for Banach space valued integrable multifunctions, Intern. J. Math. and Math. Sci. 10 (1987), 433-442. (1987) Zbl0619.28009MR0896595
  12. Papageorgiou N.S., Measurable multifunctions and their applications to convex integral functionals, Intern. J. Math. and Math. Sci. 12 (1989), 175-192. (1989) Zbl0659.28008MR0973087
  13. Papageorgiou N.S., Decomposable sets in the Lebesgue-Bochner spaces, Comment. Math. Univ. Sancti Pauli 37 (1988), 49-62. (1988) Zbl0679.46032MR0942305
  14. Papageorgiou N.S., Deterministic and random Volterra integral inclusions, Publ. de l'Institut Math. 46 (1989), 119-131. (1989) Zbl0699.45003MR1060066
  15. Papageorgiou N.S., On multivalued evolution equations and differential inclusions in Banach spaces, Comment. Math. Univ. Sancti Pauli 36 (1987), 21-39. (1987) Zbl0641.47052MR0892378
  16. Saint-Beuve M.-F., On the extension of von Neumann-Aumann's theorem, J. Funct. Anal. 17 (1974), 112-129. (1974) MR0374364
  17. Tarafdar E., Vyborny R., Fixed point theorems for condensing multivalued mappings on a locally convex topological spaces, Bull. Austr. Math. Soc. 12 (1975), 161-170. (1975) MR0383167
  18. Wagner D., Survey of measurable selection theorems, SIAM J. Control and Optim. 15 (1977), 859-903. (1977) Zbl0407.28006MR0486391

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