On generalized differential equations in Banach spaces

Tadeusz Poreda

GDML_Books, (1991), p.

Résumé

CONTENTSIntroduction . . . . . . . . 5I. 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 . . . . . . . . 8II. 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 . . . . . . . . 15III. 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 . . . . . . . . 26IV. 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 . . . . . . . . 39V. 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 . . . . . . . . 47References . . . . . . . . 49

1991 Mathematics Subject Classification: Primary 35F99, 34G99.

Détail

Zbl 0745.35048

EUDML-ID : urn:eudml:doc:219349