On some nonlinear operators in -spaces

被引：0

作者：

Bugajewski, Dariusz ^{[1
]}

Czudek, Klaudiusz ^{[2
]}

Gulgowski, Jacek ^{[2
]}

Sadowski, Jedrzej ^{[1
]}

机构：

[1] Adam Mickiewicz Univ, Optimizat & Control Theory Dept, Fac Math & Comp Sci, Ul Umultowska 87, PL-61614 Poznan, Poland

[2] Univ Gdansk, Inst Math, Fac Math Phys & Informat, PL-80308 Gdansk, Poland

来源：

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS | 2017年 / 19卷 / 04期

关键词：

Aronszajn-type theorem; compact embedding; existence theorem; linear integral operator of a Fredholm-type; nonlinear Hammerstein integral equation; superposition operator; variation in the sense of Jordan; Waterman sequence; Lambda-variation; LAMBDA-BOUNDED VARIATION; CONVERGENCE; CONTINUITY;

D O I：

10.1007/s11784-017-0450-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we investigate autonomous as well as nonautonomous superposition operators acting between spaces of functions of bounded -variation. A particular emphasis is put on acting conditions as well as on continuity problems for such operators. In particular, we give necessary and sufficient conditions for nonautonomous superposition operators to map a space of functions of bounded -variation into itself. Moreover, we prove the continuity of certain autonomous superposition operators acting between various spaces of functions of bounded -variation. We also examine the existence of -solutions as well as the topological structure of such solution sets to classical nonlinear integral equations.

引用

页码：2785 / 2818

页数：34

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