Topological Degree with Applications
暫譯: 拓撲度及其應用

Vidossich, Giovanni

Topological Degree with Applications
  • 出版商: Springer
  • 出版日期: 2026-05-22
  • 售價: $8,920
  • 貴賓價: 9.5 折 $8,474
  • 語言: 英文
  • 頁數: 574
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3031929977
  • ISBN-13: 9783031929977
  • 相關分類: 離散數學 Discrete-mathematics

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商品描述

This book is unique in the current scenario because it provides a complete treatment of modern Brouwer and of Leray-Schauder degree theories, including detailed proofs and selected applications to differential equations. In addition, new results and open problems appear throughout. It aims to introduce Ph.D. students to research on nonlinear boundary value problems for ordinary, elliptic, and evolution equations using the topological methods of nonlinear functional analysis. It is suitable for self-study, as all proofs are detailed, with prerequisites provided when necessary. It is based on personal notes compiled over more than forty years of teaching.

GV studied Mathematics in Pisa during the 1960s with G.Stampacchia as supervisor. He has been professor at the Universities of Brasilia and Trieste, ending his career at SISSA (the research institute he co-founded together with P.Budinich, L.Fonda and L.Stasi). He has held visiting positions in Brazil, Peru, Somalia, South Africa and USA. After an initial activity in General Topology, his main research topic has become BVPs of ODEs in connection with the topological methods of Nonlinear Functional Analysis.

商品描述(中文翻譯)

這本書在當前的情況下是獨特的，因為它提供了現代Brouwer和Leray-Schauder度理論的完整處理，包括詳細的證明和對微分方程的選定應用。此外，書中還出現了新的結果和未解決的問題。它旨在向博士生介紹使用非線性泛函分析的拓撲方法研究常微分方程、橢圓方程和演化方程的非線性邊值問題。這本書適合自學，因為所有證明都詳細說明，必要時提供先決條件。它基於超過四十年的教學個人筆記編寫而成。

GV在1960年代於比薩學習數學，指導教授為G.Stampacchia。他曾在巴西利亞大學和的里雅斯特大學任教，並在他共同創辦的SISSA（研究所，與P.Budinich、L.Fonda和L.Stasi共同創立）結束了他的職業生涯。他曾在巴西、秘魯、索馬利亞、南非和美國擔任訪問職位。在最初的廣義拓撲學活動之後，他的主要研究主題變成了與非線性泛函分析的拓撲方法相關的常微分方程的邊值問題（BVPs）。

作者簡介

GV studied Mathematics in Pisa during the 1960s with G.Stampacchia as supervisor. He has been professor at the Universities of Brasilia and Trieste, ending his career at SISSA (the research institute he co-founded together with P.Budinich, L.Fonda and L.Stasi). He has held visiting positions in Brazil, Peru, Somalia, South Africa and USA. After an initial activity in General Topology, his main research topic has become BVPs of ODEs in connection with the topological methods of Nonlinear Functional Analysis.

作者簡介(中文翻譯)

GV在1960年代於比薩大學（Pisa）學習數學，指導教授為G.Stampacchia。他曾擔任巴西利亞大學（Universidade de Brasilia）和的里雅斯特大學（Università di Trieste）的教授，並在他與P.Budinich、L.Fonda和L.Stasi共同創立的SISSA（國際高等科學研究所）結束了他的職業生涯。他曾在巴西、秘魯、索馬利亞、南非和美國擔任訪問職位。在最初從事一般拓撲學的研究後，他的主要研究主題轉向與非線性泛函分析的拓撲方法相關的常微分方程邊值問題（BVPs of ODEs）。

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