Nonlinear mappings of monotone type
Nonlinear mappings of monotone type
复制标题
DOI：
10.1007/978-94-009-9544-4
复制
发表时间：
1979-03
期刊：
影响因子：
--
通讯作者：
D. Pascali;S. Sburlan
中科院分区：
文献类型：
--
作者：
D. Pascali;S. Sburlan
非线性泛函分析的发展使许多非线性数学物理问题的研究成为可能。这本书提供了基本的方法和结果的调查在这方面的特殊问题。非线性分析和凸分析之间的联系产生了从Banach空间到其对偶空间的单调算子的重要领域。这些映射将紧算子的性质推广到无限维情形。单调算子的推广称为单调型映射。其中，近十年来，伪单调算子和（M）型映射为求解大类非线性微分和积分方程提供了一个更合适的工具。正文详细论述了基本上四个相互关联的主题：非线性映射的单音型，Hammerstein方程，奇算子和变分问题。为了使方法更容易，我们已经编制了一些基本结果的拓扑度和Sobolev空间。在应用中，我们只讨论非线性椭圆型方程解的存在性。目前的英文editIOn写从罗马尼亚书”Operatori neliniari”（非线性映射）的第一作者和他的演讲发表在大学的布加勒斯特和罗马。这本书的改进的最终形式是作者共同努力的结果。
The progress in nonlinear functional analysis has allowed the study of many nonlinear problems in mathematical physics. This book provides basic methods and results for the investigation of the special problems in this area. The connection between nonlinear analysis and convex analysis gave rise to the important field of monotone operators from a Banach space into its dual space. These mappings extend the properties of compact operators to the infinite-dimensional case. Generalizations of monotone operators are termed mappings of monotone type. Among these, in the last decade, the pseudo-monotone operators and the mappings of type (M) have provided a more proper tool for solving large classes of nonlinear differential and integral equations. The text dwells upon essentially four interrelated topics: Nonlinear mappings of mono tone type, Hammerstein equations, Odd operators and Variational problems. To make the approach easier, we have compiled some basic results on the topological degree and on the Sobolev spaces. In the applications we restrict our discussion to the existence of solutions for nonlinear elliptic equations. The present English editIOn was written starting from the Romanian book" Operatori neliniari"(Nonlinear Mappings) by the first author and his lectures delivered at the Universities of Bucharest and Rome. The improved final form of this book is the result of the joint work of the authors.