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]**Ju. G. Borisovič, B. D. Gel′man, A. D. Myškis, and V. V. Obuhovskiĭ,*Topological methods in the theory of fixed points of multivalued mappings*, Uspekhi Mat. Nauk**35**(1980), no. 1(211), 59–126, 255 (Russian). MR**565568****[2]**Yu. G. Borisovich, B. D. Gel′man, A. D. Myshkis, and V. V. Obukhovskiĭ,*\cyr Vvedenie v teoriyu mnogoznachnykh otobrazheniĭ*, Voronezhskiĭ Gosudarstvennyĭ Universitet, Voronezh, 1986 (Russian). MR**928179****[3]**Yu. G. Borisovich, B. D. Gel′man, A. D. Myshkis, and V. V. Obukhovskiĭ,*Multivalued analysis and operator inclusions*, Current problems in mathematics. Newest results, Vol. 29 (Russian), Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1986, pp. 151–211, 215 (Russian). MR**892745****[4]**G. Conti, P. Nistri, and P. Zecca,*Systems of set-valued equations in Banach spaces*, Delay differential equations and dynamical systems (Claremont, CA, 1990) Lecture Notes in Math., vol. 1475, Springer, Berlin, 1991, pp. 98–109. MR**1132022**, https://doi.org/10.1007/BFb0083483**[5]**-,*Non convex set-valued systems in Banach spaces*, Funkcial. Ekvac. (to appear).**[6]**Giuseppe Conti and Jacobo Pejsachowicz,*Fixed point theorems for multivalued weighted maps*, Ann. Mat. Pura Appl. (4)**126**(1980), 319–341 (1981). MR**612366**, https://doi.org/10.1007/BF01762514**[7]**Đá»— Há»“ng Tân,*On continuity of fixed points of multivalued collectively condensing mappings*, Indian J. Pure Appl. Math.**15**(1984), no. 6, 631–632. MR**750213****[8]**Lech Górniewicz,*Homological methods in fixed-point theory of multi-valued maps*, Dissertationes Math. (Rozprawy Mat.)**129**(1976), 71. MR**0394637****[9]**Andrzej Lasota and Zdzisław Opial,*An approximation theorem for multi-valued mappings*, Podstawy Sterowania**1**(1971), 71–75 (English, with Polish and Russian summaries). MR**0305336****[10]**I. Massabo, P. Nistri, and J. Pejsachowicz,*On the solvability of nonlinear equations in Banach spaces*, Fixed point theory (Sherbrooke, Que., 1980) Lecture Notes in Math., vol. 886, Springer, Berlin-New York, 1981, pp. 270–299. MR**643012****[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]**Nikolaos S. Papageorgiou,*On multivalued evolution equations and differential inclusions in Banach spaces*, Comment. Math. Univ. St. Paul.**36**(1987), no. 1, 21–39. MR**892378****[16]**B. N. Sadovskiĭ,*Limit-compact and condensing operators*, Uspehi Mat. Nauk**27**(1972), no. 1(163), 81–146 (Russian). MR**0428132****[17]**E. U. Tarafdar and H. B. Thompson,*On the solvability of nonlinear noncompact operator equations*, J. Austral. Math. Soc. Ser. A**43**(1987), no. 1, 103–126. MR**886808**

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