Theorems on the representation of nonlinear mapping families and implicit function theorems

Mathematical Notes

Volumn 67, Issue 1, 2000, Pages 45-54

  Izmailov, A F ^a  

^a RUSSIAN ACADEMY OF SCIENCES   (Russian Federation)

Author keywords

Implicit function theorems; Local nonlinear analysis; Nonlinear mappings

Indexed keywords

EID: 21044459457     PISSN: 00014346     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02675791     Document Type: Article

References (7)

1. V. M. Alekseev, V. M. Tikhomirov, and S. V. Fomin, Optimal Control [in Russian], Nauka, Moscow (1979).
2. A. F. Izmailov, "Some generalizations of the Morse lemma," Trudy Mat. Inst. Steklov [Proc. Steklov Inst. Math.], 220, 142-156 (1998).
3. E. R. Avakov, "Theorems on estimates in the neighborhood of a mapping singular point," Mat. Zametki [Math. Notes], 47, No. 5, 3-13 (1990).
4. A. D. Ioffe and V. M. Tikhomirov, Theory of Extremum Problems [in Russian], Nauka, Moscow (1974).
5. A. F. Izmailov and A. A. Tret'yakov, Quotient Analysis of Nonlinear Mappings [in Russian], Nauka, Moscow (1994).
6. E. R. Avakov, A. A. Agrachev, and A. V. Arutyunov, "A level set of a smooth mapping in the neighborhood of a singular point and zeros of a quadratic mapping," Mat. Sb. [Russian Acad. Sci. Sb. Math.], 182, No. 8, 1091-1104 (1991).
7. A. V. Arutyunov, "Implicit function theorem and abnormal points," Dokl. Ross. Akad. Nauk [Russian Acad. Sci. Dokl. Math.], 368, No. 8, 3-5 (1999).