Generalization of some MA Krasnosel'skii's results

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:428

Article

Erzakova, Nina A.¹ 

[1] Moscow State Tech Univ Civil Aviat, Moscow, Russia

关键词: Measure of noncompactness;    Condensing map;    Bifurcation point;    Nonlinear equation;    Frechet derivative;    Asymptotic derivative;   

DOI  :  10.1016/j.jmaa.2015.03.063

来源: Elsevier

【 摘 要 】

We prove necessary and sufficient conditions for complete continuity of the Frechet derivative at a point and the asymptotic derivative (in the case of their existence). For any measure of noncompactness psi, we introduce two new classes of operators: a locally strongly psi-condensing operator at a point and a strongly psi-condensing at infinity on spheres. The new classes contain all completely continuous operators and some noncondensing operators. In addition, we extend some results of M.A. Krasnosel'skii on bifurcation points to a class of vector fields more general than completely continuous. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free