|
In mathematics, topological degree theory is a generalization of the winding number of a curve in the complex plane. It can be used to estimate the number of solutions of an equation, and is closely connected to fixed-point theory. When one solution of an equation is easily found, degree theory can often be used to prove existence of a second, nontrivial, solution. There are different types of degree for different types of maps: e.g. for maps between Banach spaces there is the Brouwer degree in R''n'', the Leray-Schauder degree for compact mappings in normed spaces, the coincidence degree and various other types. There is also a degree for continuous maps between manifolds. Topological degree theory has applications in complementarity problems, differential equations, differential inclusions and dynamical systems. ==Further reading== *(Topological fixed point theory of multivalued mappings ), Lech Górniewicz, Springer, 1999, ISBN 978-0-7923-6001-8 *(Topological degree theory and applications ), Donal O'Regan, Yeol Je Cho, Yu Qing Chen, CRC Press, 2006, ISBN 978-1-58488-648-8 *(Mapping Degree Theory ), Enrique Outerelo, Jesus M. Ruiz, AMS Bookstore, 2009, ISBN 978-0-8218-4915-6 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「topological degree theory」の詳細全文を読む スポンサード リンク
|