Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-27T19:35:31.386Z Has data issue: false hasContentIssue false
  • English
  • Français

Surjectivity of multifunctions under generalized differentiability assumptions

Published online by Cambridge University Press:  17 April 2009

Serge Gautier ,
George Isac  and
Jean-Paul Penot
Serge Gautier
Affiliation:
Département de Mathématiques, Université de Pau, 64000 Pau, France;
George Isac
Affiliation:
Département de Mathématiques, Collége militaire royal, St-Jean, Québec, CanadaJOJ IRO.
Jean-Paul Penot
Affiliation:
Département de Mathématiques, Université de Pau, 64000 Pau, France;
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The aim of the present paper is to give some general surjectivity theorems for multifunctions using tangent cones and generalized differentiability assumptions.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 28 , Issue 1 , August 1983 , pp. 13 - 21
Copyright
Copyright © Australian Mathematical Society 1983

References

[1]Aubin, Jean Pierre, “Contingent derivatives of set-valued maps and existence of solutions to nonlinear inclusions and differential inclusions”, Mathematical analysis and applications, 159–229 (Advances in Mathematics, Supplementary Studies, 7a. Academic Press [Harcourt Brace Jovanich], New York, London, 1981).Google Scholar
[2]Banks, H.T. and Jacobs, Marc Q., “A differential calculus for multi-functions”, J. Math. Anal. Appl. 29 (1970), 246–272.Google Scholar
[3]Bridgland, T.F. Jr, “Trajectory integrals of set valued functions”, Pacific J. Math. 33 (1970), 43–68.Google Scholar
[4]Browder, Felix E., “On the Fredholm alternative for nonlinear operators”, Bull. Amer. Math. Soc. 76 (1970), 993–998.CrossRefGoogle Scholar
[5]Browder, F.E., “Normal solvability and existence theorems for nonlinear mappings in Banach spaces”, Problems in non-linear analysis, 17–35 (C.I.M.E., IV Ciclo, Varenna, 1970. Edizioni Cremonese, Rome, 1971).Google Scholar
[6]Browder, F.E., “Normal solvability for non-linear mappings and the geometry of Banach spaces”, Problems in non-linear analysis, 37–66 (C.I.M.E., IV Ciclo, Varenna, 1970. Edizioni Cremonese, Rome, 1971).Google Scholar
[7]Browder, Felix E., “Normal solvability and the Fredholm alternative for mappings into infinite dimensional manifolds”, J. Funct. Anal. 8 (1971), 250–274.Google Scholar
[8]Daneš, Josef, “A geometric theorem useful in nonlinear functional analysis”, Boll. Un. Mat. Ital. (4) 6 (1972), 369–375.Google Scholar
[9]De Blasi, F.S., “On the differentiability of multifunctions”, Pacific J. Math. 66 (1976), 67–81.Google Scholar
[10]Gautier, S., “Différentiabilité des multiapplications” (Publ. Math. Universite de Pau, Pau, 1978).Google Scholar
[11]Isac, G., “Sur la surjectivite des applications multivalentes differentiables”, Libertas Math. 2 (1982), 141–149.Google Scholar
[12]Hukuhara, Masus, “Intégration des applications mesurables dont la valeur est un compact convexe”, Funkcial. Ekvac. 10 (1967), 205–223.Google Scholar
[13]Chang, Kung-Ching and Shujie, Li, “A remark on expanding maps”, Proc. Amer. Math. Soc. 85 (1982), 583–586.CrossRefGoogle Scholar
[14]Makarov, V.I. and Rubinov, A.M., Mathematical theory of economics and equilibria (Springer-Verlag, Berlin, Heidelberg, New York, 1977).Google Scholar
[15]Martelli, Mario and Vignoli, Alfonso, On differentiability of multivalued maps”, Boll. Un. Mat. Ital. 10 (1974), 701–712.Google Scholar
[16]Methlouthi, Hamid, “Calcul différentiel multivoque” (Cahiers de Mathématiques de la décision No. 7702. Université de Paris, Dauphine).Google Scholar
[17]Miricǎ, Stefan, “A note on the generalized differentiability of mappings”, Nonlinear Anal. 4 (1980), 567–575.Google Scholar
[18]Nirenberg, L., Topics in nonlinear functional analysis (Courant Institute of Mathematical Sciences. New York University, New York, 1974).Google Scholar
[19]Penot, Jean-Paul, “Open mapping theorems and linearization stability”, preprint.Google Scholar
[20]Penot, Jean-Paul, “Differentiability of relations and differential stability of perturbed optimization problems”, SIAM J. Control Optim. (to appear).Google Scholar
[21]Du'o'ng, Pham Canh and Tuy, Hoàng, “Stability, surjectivity and local invertibility of non-differentiable mappings”, Acta Math. Vietnam. 3 (1978), 89–105.Google Scholar
[22]Pohožaev, S.I., “Normal solvability of nonlinear equations”, Soviet Math. Dokl. 10 (1969), 35–38.Google Scholar
[23]Похожаев, С.И. [S.I. Pohožaev], “О нелинейных операторах имеющих слабо замкную областъ значений и квазилинейных зллиптических уравнениях” [Nonlinear operators which have a weakly closed range of values, and quasilinear elliptic equations], Mat. Sb. 78 (120) (1969), 237–259.Google Scholar
[24]Похожаев, С.И. [S.I. Pohožaev], “ Нормальная разрешимость нелинейных уравнений в равномерно выпуклых Банаховых пространствах” [Normal solvability of nonlinear equations in uniformly convex Banach spaces], Funkoional Anal, i Prilozen 3 (1969), 80–84.Google Scholar
[25]Robinson, Stephen M., “Normed convex processes”, Trans. Amer. Math. Soc. 174 (1972), 127–140.Google Scholar
[26]Robinson, Stephen M., “Stability theory for systems of inequalities. Part I: Linear systems”, SIAM J. Numer. Anal. 12 (1975), 754–769.CrossRefGoogle Scholar
[27]Robinson, Stephen M., “Stability theory for systems of inequalities, Part II: differentiable nonlinear systems”, SIAM J. Numer. Anal. 13 (1976), 497–513.CrossRefGoogle Scholar