The homotopy index and partial differential equations

Krzysztof P. Rybakowski

The book presents an extension, due to the present author, of Conley's homotopy index theory to certain (one-sided) semiflows on general (not necessarily locally compact) metric spaces. This permits direct applications to say, parabolic partial differential equations, or functional differential equations. The presentation is self-contained. The subject of the book was previously presented by the author in a series of published papers.

「Nielsen BookData」より

[目次]

  • I The homotopy index theory.- 1.1 Local semiflows.- 1.2 The no blow-up condition. Convergence of semiflows.- 1.3 Isolated invariant sets and isolating blocks.- 1.4 Admissibility.- 1.5 Existence of isolating blocks.- 1.6 Homotopies and inclusion induced maps.- 1.7 Index and quasi-index pairs.- 1.8 Some special maps used in the construction of the Morse index.- 1.9 The Categorial Morse index.- 1.10 The homotopy index and its basic properties.- 1.11 Linear semiflows. Irreducibility.- 1.12 Continuation of the homotopy index.- II Applications to partial differential equations.- 2.1 Sectorial operators generated by partial differential operators.- 2.2 Center manifolds and their approximation.- 2.3 The index product formula.- 2.4 A one-dimensional example.- 2.5 Asymptotically linear systems.- 2.6 Estimates at zero and nontrivial solution of elliptic equations.- 2.7 Positive heteroclinic orbits of second-order parabolic equations.- 2.8 A homotopy index continuation method and periodic solutions of second-order gradient systems.- III Selected topics.- 3.1 Repeller-attractor pairs and Morse decompositions.- 3.2 Block pairs and index triples.- 3.3 A Morse equation.- 3.4 The homotopy index and Morse theory on Hilbert manifolds.- 3.5 Continuation of the categorial Morse index along paths.- Bibliographical notes and comments.

「Nielsen BookData」より

この本の情報

書名 The homotopy index and partial differential equations
著作者等 Rybakowski, Krzysztof P.
Rybakowski Krzysztof P
シリーズ名 Universitext
出版元 Springer-Verlag
刊行年月 c1987
版表示 Softcover reprint of the original 1st ed. 1987
ページ数 xii, 208 p.
大きさ 25 cm
ISBN 3540180672
0387180672
NCID BA00952315
※クリックでCiNii Booksを表示
言語 英語
出版国 ドイツ
この本を: 
このエントリーをはてなブックマークに追加

Yahoo!ブックマークに登録
この記事をクリップ!
Clip to Evernote
このページを印刷

外部サイトで検索

この本と繋がる本を検索

ウィキペディアから連想