Title:
|
On integral inclusions of Volterra type in Banach spaces (English) |
Author:
|
Papageorgiou, Nikolaos S. |
Language:
|
English |
Journal:
|
Czechoslovak Mathematical Journal |
ISSN:
|
0011-4642 (print) |
ISSN:
|
1572-9141 (online) |
Volume:
|
42 |
Issue:
|
4 |
Year:
|
1992 |
Pages:
|
693-714 |
. |
Category:
|
math |
. |
MSC:
|
34G20 |
MSC:
|
34K30 |
MSC:
|
45G10 |
MSC:
|
45N05 |
MSC:
|
49J24 |
idZBL:
|
Zbl 0781.45014 |
idMR:
|
MR1182201 |
DOI:
|
10.21136/CMJ.1992.128366 |
. |
Date available:
|
2009-09-24T09:25:52Z |
Last updated:
|
2020-07-29 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128366 |
. |
Reference:
|
[1] H. Attouch: Variational Convergence for Functinals and Operators.Pitman, London, 1984. |
Reference:
|
[2] J. Banas and K. Goebel: Measures of Noncompactness in Banach Spaces.Marcel Dekker, New York, 1980. MR 0591679 |
Reference:
|
[3] A. Bogatyrev: Fixed points and properties of solutions of differential inclusions.Math. USSR, Izvestia 23 (1984), 185–199. Zbl 0555.34011, MR 0712098, 10.1070/IM1984v023n01ABEH001462 |
Reference:
|
[4] A. Bressan and G. Colombo: Extensions and selections of maps with decomposable values.Studia Math. 90 (1988), 69–86. MR 0947921, 10.4064/sm-90-1-69-86 |
Reference:
|
[5] J. Diestel and J. Uhl: Vector Measures.Math. Surveys, Vol. 15, AMS, Providence, RI, 1977. MR 0453964 |
Reference:
|
[6] J. Dugundji: Topology.Allyn and Bacon, Boston, 1966. Zbl 0144.21501, MR 0193606 |
Reference:
|
[7] A. Friedman: Partial Differential Equations.Krieger, Huntington, New York, 1976. MR 0454266 |
Reference:
|
[8] K. Glashoff and J. Sprekels: An application of Glicksberg’s theorem to set-valued integral equations arising in the theory of thermostats.SIAM J. Math. Anal. 12 (1981), 477–486. MR 0613326, 10.1137/0512041 |
Reference:
|
[9] K. Glashoff and J. Sprekels: The regulation of temperature by thermostat and set-valued integral equations.J. Integral Equations 4 (1982), 95–112. MR 0654076 |
Reference:
|
[10] C. Himmelberg: Measurable relations.Fund. Math. 87 (1975), 53–72. Zbl 0296.28003, MR 0367142, 10.4064/fm-87-1-53-72 |
Reference:
|
[11] D. Kandilakis and N. S. Papageorgiou: Nonsmooth analysis and aproximation.J. Approx. Theory 52 (1988), 58–81. MR 0922594, 10.1016/0021-9045(88)90037-8 |
Reference:
|
[12] D. Kandilakis and N. S. Papageorgiou: On the properties of the Aumann integral with applications to differential inclusions and control systems.Czechoslovak Math. J. 39 (1989), 1–15. MR 0983479 |
Reference:
|
[13] D. Kandilakis and N. S. Papageorgiou: Properties of measurable multifunctions with stochastic domain and their applications.Math. Japonica 35 (1990), 629–643. MR 1067862 |
Reference:
|
[14] E. Klein and A. Thompson: Theory of Correspondences.Willey, New York, 1984. MR 0752692 |
Reference:
|
[15] G. Leitmann: Deterministic control and uncertain systems.Astronautica Acta 7 (1980), 1457–1461. 10.1016/0094-5765(80)90021-1 |
Reference:
|
[16] G. Leitmann, E. Ryan and A. Steinberg: Feedback control of uncertain systems; Robusteness with respect to neglected actuator and sensor dynamics.Intern. J. Control 43 (1986), 1243–1256. MR 0832557, 10.1080/00207178608933535 |
Reference:
|
[17] L. Lyapin: Hammerstein inclusions.Diff. Equations 12 (1976), 638–643. |
Reference:
|
[18] H. Mönch: Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces.Nonl. Anal.-TMA 4 (1980), 985–999. MR 0586861, 10.1016/0362-546X(80)90010-3 |
Reference:
|
[19] N. S. Papageorgiou: Convergence theorems for Banach space-valued integrable multifunctions.Intern. J. Math. and Math. Sci. 10 (1987), 433–442. Zbl 0619.28009, MR 0896595, 10.1155/S0161171287000516 |
Reference:
|
[20] N. S. Papageorgiou: Volterra integral inclusions in Banach spaces.J. Integral Equations and Applications 1 (1988), 65–82. Zbl 0659.45010, MR 0955163, 10.1216/JIE-1988-1-1-65 |
Reference:
|
[21] N. S. Papageorgiou: Existence and convergence results for integral inclusions in Banach spaces.J. Integral Equations and Appl. 1 (1988), 265–285. Zbl 0668.45009, MR 0978744, 10.1216/JIE-1988-1-2-265 |
Reference:
|
[22] N. S. Papageorgiou: Measurable multifunctions and their applications to convex integral functionals.Inter, J. Math. and Math. Sci. 12 (1989), 175–192. Zbl 0659.28008, MR 0973087 |
Reference:
|
[23] N. S. Papageorgiou: On the theory of Banach space valued multifunctions: Part 1: Integration and conditional expectation.J. Multiv. Anal 17 (1985), 185–206. MR 0808276, 10.1016/0047-259X(85)90078-8 |
Reference:
|
[24] N. S. Papageorgiou: Optimal control of nonlinear evolution inclusions.J. Optim. Theory and Appl. 67 (1990), 321–354. Zbl 0697.49007, MR 1080139, 10.1007/BF00940479 |
Reference:
|
[25] R. Ragimkhanov: The existence of solutions to an integral equation with multivalued right-hand side.Siberian Math. Jour. 17 (1976), 533–536. 10.1007/BF00967875 |
Reference:
|
[26] S. Szufla: On the existence of Volterra integral equations in Banach space.Bull. Polish Acad. Sci. 22 (1974), 1211–1213. MR 0380306 |
Reference:
|
[26] H. Tanabe: Equations of Evolution.Pitman, London, 1977. |
Reference:
|
[28] E. Tarafdar and R. Výborný: Fixed point theorems for condensing multivalued mappings on a locally convex topological space.Bull. Austr. Math. Soc. 12 (1975), 161–170. MR 0383167, 10.1017/S0004972700023789 |
Reference:
|
[29] R. Vaughn: Existence and comparison results for nonlinear Volterra integral equaitions in a Banach space.Appl. Anal. 7 (1978), 337–348. MR 0511320, 10.1080/00036817808839205 |
Reference:
|
[30] D. Wagner: Survey of measurable selection theorems.SIAM J. Control Optim. 15 (1977), 859–903. Zbl 0407.28006, MR 0486391, 10.1137/0315056 |
Reference:
|
[31] E. Zeidler: Nonlinear Functional Analysis and its Applications II.Springer, New York, 1990. Zbl 0684.47029, MR 0816732 |
. |