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Volumn 54, Issue 4, 2003, Pages 707-754

On the solution sets of differential inclusions and the periodic problem in Banach spaces

Author keywords

C0 semigroup; Equilibria; Initial value problem under constraints; Periodic solutions; R sets; Set valued maps

Indexed keywords

DIFFERENTIAL EQUATIONS; INITIAL VALUE PROBLEMS; MAPS; PROBLEM SOLVING;

EID: 0038356807     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(03)00098-1     Document Type: Article
Times cited : (37)

References (54)
  • 2
    • 22844456512 scopus 로고    scopus 로고
    • Topological structure of solution sets to multivalued asymptotic problems
    • Andres J., Gabor G., Górniewicz L. Topological structure of solution sets to multivalued asymptotic problems. Z. Anal. Anwendungen. 19:2000;35-60.
    • (2000) Z. Anal. Anwendungen , vol.19 , pp. 35-60
    • Andres, J.1    Gabor, G.2    Górniewicz, L.3
  • 3
    • 0036568073 scopus 로고    scopus 로고
    • Acyclicity of solution sets to functional inclusions
    • Andres J., Gabor G., Górniewicz L. Acyclicity of solution sets to functional inclusions. Nonlinear Anal. TMA. 49:2002;671-688.
    • (2002) Nonlinear Anal. TMA , vol.49 , pp. 671-688
    • Andres, J.1    Gabor, G.2    Górniewicz, L.3
  • 4
    • 0001633989 scopus 로고
    • Le correspondant topologique de l'unicite dans la théorie des équations differentielles
    • Aronszajn N. Le correspondant topologique de l'unicite dans la théorie des équations differentielles. Ann. Math. 43:1942;730-738.
    • (1942) Ann. Math. , vol.43 , pp. 730-738
    • Aronszajn, N.1
  • 6
    • 0038020778 scopus 로고    scopus 로고
    • Fixed point theorems for compositions of set-valued maps with single-valued maps
    • LI.2
    • Bader R. Fixed point theorems for compositions of set-valued maps with single-valued maps. Ann. Univ. Mariae Curie-Skłodowska, Sect. A, Lublin. LI.2:1997;29-41.
    • (1997) Ann. Univ. Mariae Curie-Skłodowska, Sect. A, Lublin , pp. 29-41
    • Bader, R.1
  • 7
    • 0038358949 scopus 로고    scopus 로고
    • The periodic problem for semilinear differential inclusions in Banach spaces
    • Bader R. The periodic problem for semilinear differential inclusions in Banach spaces. Comment. Math. Univ. Carolin. 39:1998;671-684.
    • (1998) Comment. Math. Univ. Carolin. , vol.39 , pp. 671-684
    • Bader, R.1
  • 8
    • 0013497590 scopus 로고    scopus 로고
    • On the semilinear multivalued flow under constraints and the periodic problem
    • Bader R. On the semilinear multivalued flow under constraints and the periodic problem. Comment. Math. Univ. Carolin. 41:2000;719-734.
    • (2000) Comment. Math. Univ. Carolin. , vol.41 , pp. 719-734
    • Bader, R.1
  • 9
    • 0035642861 scopus 로고    scopus 로고
    • On the solution set of constrained differential inclusions with applications
    • Bader R., Kryszewski W. On the solution set of constrained differential inclusions with applications. Set-Valued Anal. 9:2001;289-313.
    • (2001) Set-Valued Anal. , vol.9 , pp. 289-313
    • Bader, R.1    Kryszewski, W.2
  • 11
    • 0003661407 scopus 로고
    • Infinite Dimensional Topology
    • Warszawa: PWN
    • Bessaga Cz., Pełczyński J. Infinite Dimensional Topology. Monografie Mat. Vol. 58:1975;PWN, Warszawa.
    • (1975) Monografie Mat , vol.58
    • Bessaga, Cz.1    Pełczyński, J.2
  • 14
    • 0038358957 scopus 로고    scopus 로고
    • Multivalued perturbations of m-accretive differential inclusions
    • Bothe D. Multivalued perturbations of. m -accretive differential inclusions Israel J. Math. 108:1998;109-138.
    • (1998) Israel J. Math. , vol.108 , pp. 109-138
    • Bothe, D.1
  • 15
    • 0009402690 scopus 로고
    • On nonconvex perturbations of maximal monotone differential inclusions
    • Bressan A., Staicu V. On nonconvex perturbations of maximal monotone differential inclusions. Set-Valued Anal. 2:1994;415-437.
    • (1994) Set-Valued Anal. , vol.2 , pp. 415-437
    • Bressan, A.1    Staicu, V.2
  • 16
    • 0000859912 scopus 로고    scopus 로고
    • Some new viability results for semilinear differential inclusions
    • Cârja O., Vrabie I.I. Some new viability results for semilinear differential inclusions. Nonlinear Differential Equations Appl. 4:1997;401-424.
    • (1997) Nonlinear Differential Equations Appl. , vol.4 , pp. 401-424
    • Cârja, O.1    Vrabie, I.I.2
  • 19
    • 0036466677 scopus 로고    scopus 로고
    • Equilibria of set-valued maps: A variational approach
    • Ćwiszewski A., Kryszewski W. Equilibria of set-valued maps. a variational approach Nonlinear Anal. TMA. 48:2002;707-746.
    • (2002) Nonlinear Anal. TMA , vol.48 , pp. 707-746
    • Ćwiszewski, A.1    Kryszewski, W.2
  • 20
    • 0005001112 scopus 로고
    • Periodic solutions of differential equations in Banach spaces
    • Deimling K. Periodic solutions of differential equations in Banach spaces. Manuscripta Math. 24:1978;31-44.
    • (1978) Manuscripta Math. , vol.24 , pp. 31-44
    • Deimling, K.1
  • 24
    • 0003317987 scopus 로고
    • Geometry of Banach Spaces
    • Berlin: Springer
    • Diestel J. Geometry of Banach Spaces. LNM. Vol. 485:1975;Springer, Berlin.
    • (1975) LNM , vol.485
    • Diestel, J.1
  • 26
    • 0009975235 scopus 로고    scopus 로고
    • Semicontinuous differential inclusions
    • Donchev T. Semicontinuous differential inclusions. Rend. Sem. Univ. Padova. 101:1999;147-160.
    • (1999) Rend. Sem. Univ. Padova , vol.101 , pp. 147-160
    • Donchev, T.1
  • 28
    • 84968494818 scopus 로고
    • A degree theory, fixed point theorems, and mapping theorems for multivalued noncompact mappings
    • Fitzpatrick P.M., Petryshyn W.V. A degree theory, fixed point theorems, and mapping theorems for multivalued noncompact mappings. Trans. Amer. Math. Soc. 194:1974;1-25.
    • (1974) Trans. Amer. Math. Soc. , vol.194 , pp. 1-25
    • Fitzpatrick, P.M.1    Petryshyn, W.V.2
  • 29
    • 0038020779 scopus 로고
    • Homological methods in fixed point theory of multivalued maps
    • Górniewicz L. Homological methods in fixed point theory of multivalued maps. Diss. Math. (Warszawa). CXXIX:1976;1-66.
    • (1976) Diss. Math. (Warszawa) , vol.129 , pp. 1-66
    • Górniewicz, L.1
  • 30
    • 0000542515 scopus 로고
    • Topological approach to differential inclusions
    • A. Granas, & M. Frigon. Topological Methods in Differential Equations and Inclusions, Dordrecht: Kluwer Academic Publishers
    • Górniewicz L. Topological approach to differential inclusions. Granas A., Frigon M. Topological Methods in Differential Equations and Inclusions. NATO ASI Series C. Vol. 472:1995;129-190 Kluwer Academic Publishers, Dordrecht.
    • (1995) NATO ASI Series C , vol.472 , pp. 129-190
    • Górniewicz, L.1
  • 33
    • 0020834187 scopus 로고
    • Periodic solutions of functional differential inclusions and fixed points of σ-selectionable correspondences
    • Haddad G., Lasry J.M. Periodic solutions of functional differential inclusions and fixed points of. σ -selectionable correspondences J. Math. Anal. Appl. 96:1983;295-312.
    • (1983) J. Math. Anal. Appl. , vol.96 , pp. 295-312
    • Haddad, G.1    Lasry, J.M.2
  • 34
    • 0007167995 scopus 로고
    • On the topological regularity of the solution set of differential inclusions with constraints
    • Hu S., Papageorgiou N.S. On the topological regularity of the solution set of differential inclusions with constraints. J. Differential Equations. 107:1994;280-290.
    • (1994) J. Differential Equations , vol.107 , pp. 280-290
    • Hu, S.1    Papageorgiou, N.S.2
  • 36
    • 0002692411 scopus 로고
    • On decreasing sequences of compact absolute retracts
    • Hyman D.M. On decreasing sequences of compact absolute retracts. Fund. Math. 64:1969;91-97.
    • (1969) Fund. Math. , vol.64 , pp. 91-97
    • Hyman, D.M.1
  • 37
    • 0013476867 scopus 로고
    • On conditions on right hand sides of differential relations
    • Jarnik J., Kurzweil J. On conditions on right hand sides of differential relations. Casopis Pest. Mat. 102:1977;334-349.
    • (1977) Casopis Pest. Mat. , vol.102 , pp. 334-349
    • Jarnik, J.1    Kurzweil, J.2
  • 38
    • 0037682915 scopus 로고    scopus 로고
    • On the translation multioperator along the solutions of semilinear differential inclusions in Banach spaces
    • Kamenski M., Obukhovski V., Zecca P. On the translation multioperator along the solutions of semilinear differential inclusions in Banach spaces. Canad. Appl. Math. Qrt. 6:1998;139-154.
    • (1998) Canad. Appl. Math. Qrt. , vol.6 , pp. 139-154
    • Kamenski, M.1    Obukhovski, V.2    Zecca, P.3
  • 40
    • 1842540579 scopus 로고
    • Homotopy invariants for set-valued maps: Homotopy-approximation approach
    • M.A. Théra, & J.-B. Baillon. London: Longman
    • Kryszewski W. Homotopy invariants for set-valued maps: homotopy-approximation approach. Théra M.A., Baillon J.-B. Fixed Point Theory and Applications. Pitman Research Notes in Mathematics Series. Vol. 252:1991;269-284 Longman, London.
    • (1991) Fixed Point Theory and Applications, Pitman Research Notes in Mathematics Series , vol.252 , pp. 269-284
    • Kryszewski, W.1
  • 41
    • 0038040761 scopus 로고    scopus 로고
    • Graph approximation of set-valued maps on non-compact spaces
    • Kryszewski W. Graph approximation of set-valued maps on non-compact spaces. Topology Appl. 83:1997;1-21.
    • (1997) Topology Appl. , vol.83 , pp. 1-21
    • Kryszewski, W.1
  • 43
    • 0038697163 scopus 로고
    • Nonlinear operators and differential equations in banach spaces
    • New York: Wiley
    • Martin H.M. Jr. Nonlinear Operators and Differential Equations in Banach Spaces, Pure & Applied Mathematics. 1976;Wiley, New York.
    • (1976) Pure & Applied Mathematics
    • Martin H.M., Jr.1
  • 45
    • 0000703026 scopus 로고
    • The fixed point index for local condensing maps
    • Nussbaum R.D. The fixed point index for local condensing maps. Ann. Mat. Pura Appl. 89:1971;217-258.
    • (1971) Ann. Mat. Pura Appl. , vol.89 , pp. 217-258
    • Nussbaum, R.D.1
  • 46
    • 0038020772 scopus 로고    scopus 로고
    • On some properties od dissipative functional differential inclusions in a Banach space
    • Obukhovski V., Zecca P. On some properties od dissipative functional differential inclusions in a Banach space. Topology Meth. Nonlinear Anal. 15:2000;369-384.
    • (2000) Topology Meth. Nonlinear Anal. , vol.15 , pp. 369-384
    • Obukhovski, V.1    Zecca, P.2
  • 48
    • 84968494115 scopus 로고
    • Fixed point theorems for various classes of 1-set-contractive and 1-ball-contractive mappings in Banach spaces
    • Petryshyn W.V. Fixed point theorems for various classes of 1-set-contractive and 1-ball-contractive mappings in Banach spaces. Trans. Amer. Math. Soc. 182:1973;323-352.
    • (1973) Trans. Amer. Math. Soc. , vol.182 , pp. 323-352
    • Petryshyn, W.V.1
  • 49
    • 0000887305 scopus 로고
    • Periodic solutions of differential inclusions on compact subsets of ℝ′
    • n J. Math. Anal. Appl. 148:1990;202-212.
    • (1990) J. Math. Anal. Appl. , vol.148 , pp. 202-212
    • Plaskacz, S.1
  • 50
    • 0000617217 scopus 로고
    • Periodic solutions of semilinear evolution equations
    • Prüss J. Periodic solutions of semilinear evolution equations. Nonlinear Anal. 3:1979;601-612.
    • (1979) Nonlinear Anal. , vol.3 , pp. 601-612
    • Prüss, J.1
  • 51
    • 0000670389 scopus 로고
    • Clarke's tangent cones and boundaries of closed sets in ℝ′
    • Rockafellar R.T. Clarke's tangent cones and boundaries of closed sets in. ℝ′ Nonlinear Anal. 3:1979;145-154.
    • (1979) Nonlinear Anal. , vol.3 , pp. 145-154
    • Rockafellar, R.T.1
  • 52
    • 0013506199 scopus 로고
    • Scorza-Dragoni type theorems for upper semicontinuous multivalued functions
    • Rzeżuchowski T. Scorza-Dragoni type theorems for upper semicontinuous multivalued functions. Bull. Acad. Polon. Sci. 8:1980;61-67.
    • (1980) Bull. Acad. Polon. Sci. , vol.8 , pp. 61-67
    • Rzezuchowski, T.1


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