Author | Rybakowski, Krzysztof P. author |
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Title | The Homotopy Index and Partial Differential Equations [electronic resource] / by Krzysztof P. Rybakowski |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1987 |
Connect to | http://dx.doi.org/10.1007/978-3-642-72833-4 |
Descript | XII, 208 p. online resource |
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