On the solvability of systems of inclusions involving noncompact operators

Authors:
P. Nistri, V. V. Obukhovskiĭ and P. Zecca

Journal:
Trans. Amer. Math. Soc. **342** (1994), 543-562

MSC:
Primary 47H15; Secondary 34G20, 34K30, 47H04, 47N20, 47N70, 49J45

DOI:
https://doi.org/10.1090/S0002-9947-1994-1232189-0

MathSciNet review:
1232189

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We consider the solvability of a system

**[1]**Yu. G. Borisovich, B. D. Gel'man, A. D. Myskis, and V. V. Obukhovskiĭ,*Topological methods in fixed-point theory of multivalued mappings*, Uspekhi Mat. Nauk**35**(1980), 59-126; English transl. in Russian Math. Surveys**35**(1980), 65-143. MR**565568 (81e:55004)****[2]**-,*Introduction to the theory of multivalued mappings*, Voronezh Univ. Press, Voronezh, (1986); English transl. in J. Soviet Math.**39**(1987), 2772-2811. MR**928179 (89f:49014)****[3]**-,*Multivalued analysis and operator inclusions*, Ser. Sov. Probl. Mat. Noveishie Dostizheniya, vol. 29, Itogi Nauki i Tekhniki, 1986, pp. 151-211. (Russian) MR**892745 (88k:58014)****[4]**G. Conti, P. Nistri, and P. Zecca,*Systems of set-valued equations in Banach spaces*, Delay Differential Equations and Dynamical Systems (Proc. Claremont 1990), (S. Busenberg and M. Martelli, eds.), Lecture Notes in Math., vol. 1475, Springer-Verlag, 1991, pp. 98-109. MR**1132022 (93e:34087)****[5]**-,*Non convex set-valued systems in Banach spaces*, Funkcial. Ekvac. (to appear).**[6]**G. Conti and J. Pejsachowicz,*Fixed points theorems for multivalued weighted maps*, Ann. Mat. Pura Appl.**126**(1980), 319-341. MR**612366 (82f:55002)****[7]**Do Hong Tan,*On continuity of fixed points of multivalued collectively condensing mappings*, Indian J. Pure Appl. Math.**15**(1984), 631-632. MR**750213 (86b:54049)****[8]**L. Gorniewicz,*Homological methods in fixed point theory of multivalued mappings*, Dissertationes Math.**129**(1976), 1-71. MR**0394637 (52:15438)****[9]**A. Lasota and Z. Opial,*An approximation theorem for multivalued mappings*, Podstawy Sterowania**1**(1971), 71-75. MR**0305336 (46:4466)****[10]**I. Massabò, P. Nistri, and J. Pejsachowicz,*On the solvability of nonlinear equations in Banach spaces*, Fixed Point Theory, (Proc. Sherbrooke, Quebec 1980), (E. Fadell and G. Fournier, eds.), Lecture Notes in Math., vol. 886, Springer-Verlag, 1980, pp. 270-289. MR**643012 (83a:47068)****[11]**V. V. Obukhovskiĭ,*Some fixed-point principles for multi-valued condensing operators*, Voronezh. Gos. Univ. Trudy Mat. Fak.**4**(1970), 70-79. (Russian)**[12]**-,*On the topological degree for a class of non compact multivalued mappings*, Funktsional Anal.**23**(1984), 82-93. (Russian)**[13]**-,*On semi-linear functional differential inclusions in a Banach space and control systems of a parabolic type*, Avtomatika**3**(1991), 73-81. (Russian)**[14]**V. V. Obukhovskiĭ and E. V. Gorokhov,*On the definition of the rotation of a class of compactly restrictible multivalued vector fields*, Voronezh. Gos. Univ. Trudy Mat. Fak.**12**(1974), 45-54. (Russian)**[15]**N. S. Papageorgiou,*On multi-valued evolution equations and differential inclusions in Banach spaces*, Comment. Math. Univ. St. Paul.**36**(1987), 21-39. MR**892378 (89f:34020)****[16]**B. N. Sadovskiĭ,*Limit-compact and condensing operators*, Uspekhi Mat. Nauk**27**(1972), no. 1, 81-146. (Russian) MR**0428132 (55:1161)****[17]**E. U. Tarafdar and H. B. Thompson,*On the solvability of nonlinear noncompact operator equations*, J. Austral. Math. Soc. Ser. A**43**(1987), 103-126. MR**886808 (88g:47123)**

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC:
47H15,
34G20,
34K30,
47H04,
47N20,
47N70,
49J45

Retrieve articles in all journals with MSC: 47H15, 34G20, 34K30, 47H04, 47N20, 47N70, 49J45

Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1994-1232189-0

Keywords:
Condensing multivalued map,
degree theory,
Borsuk-Ulam condition,
control problem,
periodic solution

Article copyright:
© Copyright 1994
American Mathematical Society