A. Georgieva
H. Kiskinov

Existence of solutions of nonlinear differential equations with generalized dichotomous linear part in a Banach space

The paper is published: Rostocker Mathematisches Kolloquium, Rostock. Math. Kolloq. 66, 75 - 85 (2011)

MSC: 34G10   Linear equations [See also 47D06, 47D09]
  34G20   Nonlinear equations [See also 47Hxx, 47Jxx]

Abstract:   A generalization of the well known dichotomies for a class of homogeneous differential equations in an arbitrary Banach space is introduced. The aim of this paper is the consideration of the nonlinear differential equation with generalized dichotomous linear part. By the help of the fixpoint principle of Banach and Schauder-Tychonoff are found sufficient conditions for the existence of solutions of the nonlinear equation.

Keywords:   Ordinary Differential Equations, Generalized Dichotomy

Seite generiert am 03.04.2012,   11:04   Uhr