Existence of solutions for operator inclusions : a unified approach
Diego Averna; Salvatore A. Marano
Rendiconti del Seminario Matematico della Università di Padova (1999)
- Volume: 102, page 285-303
- ISSN: 0041-8994
Access Full Article
topHow to cite
topAverna, Diego, and Marano, Salvatore A.. "Existence of solutions for operator inclusions : a unified approach." Rendiconti del Seminario Matematico della Università di Padova 102 (1999): 285-303. <http://eudml.org/doc/108506>.
@article{Averna1999,
author = {Averna, Diego, Marano, Salvatore A.},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {operator inclusions with multivalued terms; mixed semicontinuity hypotheses; existence of solutions; Bressan and Colombo's directionally continuous selection theorem; Ky Fan's fixed point principle; Cauchy problem},
language = {eng},
pages = {285-303},
publisher = {Seminario Matematico of the University of Padua},
title = {Existence of solutions for operator inclusions : a unified approach},
url = {http://eudml.org/doc/108506},
volume = {102},
year = {1999},
}
TY - JOUR
AU - Averna, Diego
AU - Marano, Salvatore A.
TI - Existence of solutions for operator inclusions : a unified approach
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1999
PB - Seminario Matematico of the University of Padua
VL - 102
SP - 285
EP - 303
LA - eng
KW - operator inclusions with multivalued terms; mixed semicontinuity hypotheses; existence of solutions; Bressan and Colombo's directionally continuous selection theorem; Ky Fan's fixed point principle; Cauchy problem
UR - http://eudml.org/doc/108506
ER -
References
top- [1] J.-P. Aubin - A. CELLINA, Differential Inclusions, Springer-Verlag, Berlin (1984). Zbl0538.34007MR755330
- [2] D. Averna, Lusin type theorems for multifunctions, Scorza Dragoni's property and Carathéodory selections, Boll. Un. Mat. Ital.A (7), 8 (1994), pp. 193-202. Zbl0817.28007MR1288374
- [3] D. Averna - G. Bonanno, Existence of solutions for a multivalued boundary value problem with non-convex and unbounded right-hand side, Ann. Polon. Mat., 71 (1999), pp. 253-271. Zbl0935.34009MR1704302
- [4] D. Averna - S.A. Marano, Existence theorems for inclusions of the type Ψ(u)(t)∈F(t, Φ(u)(t)), Appl. Anal., to appear. Zbl1027.47063
- [5] G. Bonanno - S.A. Marano, Higher order ordinary differential equations, Differential Integral Equations, 6 (1993), pp. 1119-1123. Zbl0785.34021MR1230485
- [6] G. Bonanno - S.A. Marano, Positive solutions of elliptic equations with discontinuous nonlinearities, Topol. Methods Nonlinear Anal., 8 (1996), pp. 263-273. Zbl0891.35038MR1483627
- [7] A. Bressan, Upper and lower semicontinuous differential inclusions: A unified approach, in: H. J. Sussman (ed.), Nonlinear Controllability and Optimal Control, Pure Appl. Math., 133, Dekker, New York (1990), pp. 21-31. Zbl0704.49011MR1061382
- [8] A. Bressan - G. Colombo, Selections and representations of multifunctions in paracompact spaces, Studia Math., 102 (1992), pp. 209-216. Zbl0807.54020MR1170551
- [9] M. Day, Normed Linear Spaces, Springer-Verlag, Berlin (1962). Zbl0082.10603
- [10] K. Deimling, Multivalued Differential Equations, de Gruyter Ser. Nonlinear Anal. Appl.1, de Gruyter, Berlin (1992). Zbl0760.34002MR1189795
- [11] C.J. Himmelberg, Measurable relations, Fund. Math., 87 (1975), pp. 53-72. Zbl0296.28003MR367142
- [12] C.J. Himmelberg - F. S. VAN VLECK, Existence of solutions for generalized differential equations with unbounded right-hand side, J. Differential Equations, 61 (1986), pp. 295-320. Zbl0582.34002MR829366
- [13] S. Lojasiewicz (jr.), Some theorems of Scorza Dragoni type for multifunctions with application to the problem of existence of solutions for differential multivalued equations, in: C. OLECH - B. JAKUBCZYK - J. ZABCZYK (eds), Mathematical Control Theory, Banach Center Publ., 14, PWN, Warsaw (1985), pp. 625-643. Zbl0576.49024MR851255
- [14] A. Majorana - S.A. Marano, Boundary value problems for higher order ordinary differential equations, Comment. Math. Univ. Carolin., 35 (1994), pp. 451-466. Zbl0809.34034MR1307273
- [15] S.A. Marano, Existence theorems for a multivalued boundary value problem, Bull. Austral. Math. Soc., 45 (1992), pp. 249-260. Zbl0741.34008MR1155483
- [16] O. NaselliRICCERI - B. RICCERI, An existence theorem for inclusions of the type W(u)(t) ∈ F(t, Φ(u)(t)) and application to a multivalued boundary value problem, Appl. Anal., 38 (1990), pp. 259-270. Zbl0687.47044
- [17] C. Olech, Existence of solutions of non-convex orientor fields, Boll. Un. Mat. Ital. (4), 11 (1975), pp. 189-197. Zbl0322.34002MR394372
- [18] E. Schechter, A survey of local existence theories for abstract nonlinear initial value problems, in: T. L. GILL - W. W. ZACHARY (eds), Nonlinear Semigroups, Partial Differential Equations and Attractors, Lecture Notes in Math.1394, Springer-Verlag, Berlin (1987), pp. 136-184. Zbl0678.34005MR1021021
- [19] A.A. Tolstonogov, Solutions of a differential inclusion with unbounded right-hand side, Siberian Math. J., 29 (1988), pp. 857-868. Zbl0702.34019MR971244
- [20] R.L. Wheeden - A. Zygmund, Measure and Integral, Monographs Textbooks Pure Appl. Math., 43, Dekker, New York (1977). Zbl0362.26004MR492146
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.