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## On generalized differential equations in Banach spaces

Autorzy
Seria
Rozprawy Matematyczne tom/nr w serii: 310 wydano: 1991
Zawartość
Warianty tytułu
Abstrakty
EN
CONTENTS
Introduction . . . . . . . . 5
I. Fundamental problems for generalized differential equations at nonsingular points
§1. Introduction . . . . . . . . 6
§2. Cauchy problem at nonsingular points for generalized differential equations of the first order . . . . . . . . 6
§3. Dependence of solution on parameters and initial conditions . . . . . . . . 8
II. Total solutions of generalized linear differential equations
§1. Introduction . . . . . . . . 11
§2. Form of solutions of generalized linear differential equations . . . . . . . . 11
§3. Stability of generalized linear differential equations . . . . . . . . 15
III. Fundamental problems for generalized differential equations at singular points
§1. Introduction . . . . . . . . 19
§2. Initial conditions at singular points and dependence of solutions upon initial conditions and parameters . . . . . . . . 19
§3. Form of solutions in a vicinity of a singular point . . . . . . . . 26
IV. Existence and form of solutions of generalized linear differential equations connected with geometrical properties of holomorphic mappings
§1. Introduction . . . . . . . . 29
§2. Holomorphic solutions of generalized differential equation connected with spiral-like mappings . . . . . . . . 31
§3. Existence and form of solutions of generalized differential equations which define close-to-starlike mappings . . . . . . . . 37
§4. Univalent subordination chains and solutions of a generalized equation of Löwner . . . . . . . . 39
V. The generalized form of the Frobenius theorem
§1. Introduction . . . . . . . . 44
§2. A necessary condition and a sufficient condition for existence and uniqueness . . . . . . . . 45
§3. The generalized Frobenius equation and its integrability conditions in Euclidean spaces . . . . . . . . 47
References . . . . . . . . 49
Słowa kluczowe
Tematy
Kategoryzacja MSC:
Miejsce publikacji
Warszawa
Seria
Rozprawy Matematyczne tom/nr w serii: 310
Liczba stron
50
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCCX
Daty
wydano
1991
otrzymano
1989-12-28
poprawiono
1991-01-10
Twórcy
autor
• Institute of Mathematics, Technical University of Łódź, Al. Politechniki 11, 90-924 Łódź, Poland
Bibliografia
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• [Pf] J. A. Pfaltzgraff, Subordination chains and univalence of holomorphic mappings on $ℂ^n$, Math. Ann. 210 (1974), 55-68.
• [PS] J. A. Pfaltzgraff and T. J. Suffridge, Close-to-starlike holomorphic functions of several variables, Pacific J. Math. 57 (1975), 271-279.
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• [Po1] T. Poreda, Generalized differential equations for maps of Banach spaces, Comment. Math. 30 (1) (1990), 141-146.
• [Po2] T. Poreda, On the geometrical properties of starlike maps of Banach spaces, submitted.
• [Po3] T. Poreda, On some topological properties of the class of normalized and starlike maps of the unit polydisc in $ℂ^n$, Acta. Univ. Lodz. Folia Math. 3 (1989), 87-93.
• [Po4] T. Poreda, On the univalent subordination chains of holomorphic mappings in Banach spaces, Comment. Math. 28 (2) (1989), 295-304.
• [Po5] T. Poreda, On the univalent holomorphic maps of the unit polydisc in $ℂ^n$ which have the parametric representation I - the geometrical properties, Ann. Univ. Mariae Curie-Skłodowska Sect. A 41 (1987), 105-113.
• [Po6] T. Poreda, On the univalent holomorphic maps of the unit polydisc in $ℂ^n$ which have the parametric representation II - the necessary conditions and the sufficient conditions, ibid., 114-121.
• [PoS] T. Poreda and A. Szadkowska, On the holomorphic solutions of certain differential equations of first order for the mappings of the unit ball in $ℂ^n$ into $ℂ^n$, Demonstratio Math. 22 (4) (1989), 983-996.
• [Se] Z. Semadeni, Banach Spaces of Continuous Functions, PWN, Warszawa 1971.
• [Su] T. J. Suffridge, Starlike and convex maps in Banach spaces, Pacific J. Math. 46 (1973), 575-589.
• [Su1] T. J. Suffridge, Starlikeness, convexity and other geometric properties of holomorphic maps in higher dimensions, in: Complex Analysis, Kentucky 1976, Lecture Notes in Math. 599, Springer 1977, 146-159.
Języki publikacji
 EN
Uwagi
1991 Mathematics Subject Classification: Primary 35F99, 34G99.