Some inverse mapping theorems
Annales de l'I.H.P. Analyse non linéaire, Tome 7 (1990) no. 3, pp. 183-234.
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     author = {Frankowska, H\'el\`ene},
     title = {Some inverse mapping theorems},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {183--234},
     publisher = {Gauthier-Villars},
     volume = {7},
     number = {3},
     year = {1990},
     mrnumber = {1065873},
     zbl = {0727.26014},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_1990__7_3_183_0/}
}
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Frankowska, Hélène. Some inverse mapping theorems. Annales de l'I.H.P. Analyse non linéaire, Tome 7 (1990) no. 3, pp. 183-234. http://www.numdam.org/item/AIHPC_1990__7_3_183_0/

[1] J.-P. Aubin, Lipschitz Behavior of Solutions to Convex Minimization Problems, Math. Operat. Res., Vol. 9, 1984, pp. 87-111. | MR | Zbl

[2] J.-P. Aubin and A. Cellina, Differential Inclusions, Springer-Verlag (Grundlehren der Math. Wissenscharften), Vol. 264, 1984. | MR | Zbl

[3] J.-P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhäuser, Berlin, Boston, 1990. | MR | Zbl

[4] J.-P. Aubin and H. Frankowska, On inverse function theorems for set-valued maps, J. Math. Pure Appl., Vol. 66, 1987, pp. 71-89. | MR | Zbl

[5] P. Beauzamy, Introduction to Banach spaces and their Geometry, North Holland Mathematics study, Vol. 68, 1985. | MR | Zbl

[6] R.M. Bianchini and G. Stefani, Sufficient Conditions of Local Controllability, Preprint Istituto Matematico Ulisse Dini 1986.

[7] J.F. Bonnans and E. Casas, Optimal Control of Semilinear Multistate Systems with State Constraints, SIAM J, Control Optimi., Vol. 27, 1989, pp. 446-455. | MR | Zbl

[8] F F. Clarke,On the Inverse Function Theorem, Pac. J. Math., Vol. 64, 1976, pp. 97- 102. | MR | Zbl

[9] F. Clarke, Optimization and Nonsmooth Analysis, Wiley Interscience, 1983. | MR | Zbl

[10] B.D. Craven and M.Z. Nashed, Generalized Implicit Function Theorems when the Derivative has no Bounded Inverse, Nonlinear Analysis, Vol. 6, 1982, pp. 375-387. | MR | Zbl

[11] A.V. Dmitruk, A.A. Milyutin and N.P. Osmolovskii, Ljustemik's Theorem and the Theory of Extrema, Uspekhi Mat. Nauk., Vol. 35:6, 1980, pp. 11-46; Russian Math. Surveys, Vol. 35:6, 1980, pp. 11-51. | MR | Zbl

[12] I. Ekeland, On the Variational Principle, J. Math. Anal. Appl., Vol. 47, 1974, pp. 324- 358. | MR | Zbl

[13] I. Ekeland, Nonconvex Minimization Problems, Bull. Am. Math. Soc., Vol. 1, 1979, pp. 443-474. | MR | Zbl

[14] H. Fattorini, A Unified Theory of Necessary Conditions for Nonlinear Non-convex Control Systems, Applied Math. Optimiz., Vol. 15, 1986, pp. 141-185. | MR | Zbl

[15] H. Fattorini and H. Frankowska, Necessary Conditions for Infinite Dimensional Control Problems, Mathematics of Systems, Signals and Control, 1991. | MR | Zbl

[16] H. Frankowska, Théorèmes d'application ouverte et de fonction inverse, C. R. Acad. Sci., Paris, Vol. 305, 1987, pp. 773-776. | MR | Zbl

[17] H. Frankowska, High Order Inverse Function Theorems, Analyse non linéaire, Proceedings of the Conference on Applied Nonlinear Analysis, Perpignan, June 22-26, 1987, Gauthier-Villars, Paris, 1989. | EuDML | Numdam | Zbl

[18] H. Frankowska, An Open Mapping Principle for Set-valued Maps, J. Math. Anal. Appl., Vol. 127, 1987, pp. 172-180. | MR | Zbl

[19] H. Frankowska, Local Controllability of Control Systems with Feedback, J. Optimiz. Theor. Appl., Vol. 60, 1989, pp. 277-296. | MR | Zbl

[20] H. Frankowska, Local Controllability and Infinitesimal Generators of Semi-groups of Set-valued Maps, SIAM J., Control Optimiz., Vol. 25, 1987, pp. 412-432. | MR | Zbl

[21] H. Frankowska, The Maximum Principle for an Optimal Solution to a Differential Inclusion with end Point Constraints, SIAM J., Control Optimiz., Vol. 25, 1987, pp. 145-157. | MR | Zbl

[22] H. Frankowska, The First Order Necessary Conditions for Nonsmooth Variational and Control Problems, SIAM J., Control Optimiz., Vol. 22, 1984, pp. 1-12. | MR | Zbl

[23] H. Frankowska, Set-valued Analysis and Some Control Problems, Modem Optimal Control, Proceedings of the International Conference "30 years of Modern Control Theory", Kingston, June 3-6, 1988, E. Roxin Editor, Marcel Dekker, New York, Basel, 1989. | MR | Zbl

[24] L.M. Graves, Some Mapping Theorem, Duke Math. J., Vol. 17, 1950, pp. 111-114. | MR | Zbl

[25] K. Grasse, A Higher-order Sufficient Condition for Local Surjectivity, Nonlinear Analysis, Vol. 10, 1986, pp. 87-96. | MR

[26] A.D. Ioffe, Regular Points of Lipschitz Functions, Trans. Am. Math. Soc., Vol. 251, 1979, pp. 61-69. | MR | Zbl

[27] A.D. Ioffe, Nonsmooth Analysis: Differential Calculus of Nondifferentiable Mappings, Trans. Am. Math. Soc., 266, 1981, pp. 1-56. | MR | Zbl

[28] A.E. Ioffe, On the Local Surjection property, Nonlinear Analysis, Vol. 11, 1987, pp. 565-592. | MR | Zbl

[29] C. Kuratowski, Topologie, Panstwowe Wydawnictwo Naukowe, 1958. | MR | Zbl

[30] E.B. Lee and L. Markus, Foundations of Optimal Control Theory. John Wiley, New York 1967. | MR | Zbl

[31] L.A. Ljusternik, Conditional Extrema of Functionals, Mat. Sb., Vol. 41, 1934, pp. 390-401.

[32] L.A. Ljusternik and V.I. Sobolev, Elementy Funktsionalnogo Analiza, Second ed., Nauka Moskow, 1965 (in Russian). | MR

[33] K. Magnusson, A.J. Pritchard and M.D. Quinn, The Application of Fixed Point to Global Nonlinear Controllability Problems, Mathematical Control Theory, Banach Center Publications, Vol. 14, 1985, pp. 319-344. | MR | Zbl

[34] K. Magnusson and A.J. Pritchard, Local Exact Controllability of Non-linear Evolution Equations, Recent Advances in Differential Equations, Academic Press, 1981, Vol. 271, pp. 271-280. | MR | Zbl

[35] J. Necas, Les méthodes directes en théorie des équations elliptiques, Masson, Paris, 1967. | MR | Zbl

[36] A. Pazy, Semi-groups of linear operators and applications to partial differential equations, Spinger, Berlin, 1978. | Zbl

[37] S. Robinson, Perturbed Kuhn-Tucker Points and Rates of Convergence for a Class of Nonlinear-programming Algorithms, Math. Programming, Vol. 7, 1974, pp. 1-16. | MR | Zbl

[38] R.T. Rockafellar, Lipschitzian Properties of Multifunctions, Non-linear Analysis, T.M.A., 9, 1985, pp. 867-885. | MR | Zbl

[39] H. Sussmann, A Sufficient Condition for Local Controllability, SIAM J., Control Optimiz., Vol. 16, 1978, pp. 790-802. | MR | Zbl

[40] J. Treiman, Characterization of Clarke's Tangent and Normal Cones in Finite and Infinite Dimension, Nonlinear Analysis, Vol. 7, 1983, pp. 771-783. | MR | Zbl

[41] J. Warga, Necessary Conditions Without Differentiability Assumptions in Optimal Control, J. Differ. Equations, Vol. 18, 1975, pp. 41-62. | MR | Zbl

[42] J. Warga, Derivate Containers, Inverse Functions and Controllability, in Calculus of Variations and Control Theory, D. L. RUSSEL, Ed., Academic Press, New York, 1976, pp. 13-46. | MR | Zbl

[43] J. Warga, Optimization and Controllability Without Differentiability Assumptions, SIAM J. Control Optimiz., Vol. 21, 1983, pp. 837-855. | MR | Zbl