Title | Topological Nonlinear Analysis [electronic resource] : Degree, Singularity, and Variations / edited by Michele Matzeu, Alfonso Vignoli |
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Imprint | Boston, MA : Birkhรคuser Boston, 1995 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-2570-6 |
Descript | 531 p. online resource |
Variational Methods and Nonlinear Problems: Classical Results and Recent Advances -- โข Introduction -- โข Lusternik-Schnirelman Theory -- โข Applications to Nonlinear Eigenvalues -- โข Unbounded Functionals -- โข Elliptic Dirichlet Problems -- โข Singular Potentials -- โข References -- to Morse Theory: A New Approach -- โข Introduction -- โข Contents -- โข The Abstract Theory -- โข The Morse Index -- โข The Poincarรฉ Polynomial -- โข The Conley Blocks -- โข The Morse Relations -- โข Morse Theory for Degenerate Critical Points -- โข Some Existence Theorems -- โข An Application to Riemannian Geometry -- โข Riemannian Manifolds -- โข Geodesies -- โข The Morse Theory for Geodesics -- โข The Index Theorem -- โข An Application to Space-Time Geometry -- โข Introduction -- โข Some Examples of Lorentzian Manifolds -- โข Morse Theory for Lorentzian Manifolds -- โข Preliminary Lemmas -- โข Proof of The Morse Relations For Static Space-Time -- โข Some Application to a Semilinear Elliptic Equation -- โข Introduction -- โข The Sublinear Case -- โข The Superlinear Case Morse Relations for Positive Solutions -- โข The Functional Setting -- โข Some Hard Analysis -- โข The Photography Method -- โข The Topology of The Strip -- โข References -- Applications of Singularity Theory to the Solutions of Nonlinear Equations -- โข The Full Lyapunov-Schmidt Reduction -- โข Matherโs Theory of C?-Stability of Mappings - Global Theory -- โข Matherโs Local Theory as Paradigm -- โข Singularity Theory with Special Conditions -- โข The Structure of Nonlinear Fredholm Operators -- โข Multiplicities of Solutions to Nonlinear Equations -- โข The Theory for Topological Equivalence -- โข Bibliography -- Fixed Point Index Calculations and Applications -- โข The Fixed Point Index -- โข Some Remarks on Convex Sets -- โข A Basic Index Calculation -- โข Index Calculations in Product Cones -- โข Applications of Index Formulae - I -- โข Applications of Index Formulae - II -- โข Some Global Branches -- โข Monotone Dynamical Systems -- โข Preliminaries -- โข Connecting Orbits and Related Results -- โข Generic Convergence -- โข References -- Topological Bifurcation -- โข Abstract -- โข Introduction -- โข Preliminaries -- โข One Parameter Bifurcation -- โข Local Bifurcation -- โข Global Bifurcation -- โข Special Nonlinearities -- โข Multiparameter Bifurcation -- โข Sufficient Conditions for Local Bifurcation -- โข Necessary Conditions for Linearized Local Bifurcation -- โข Multiparameter Global Bifurcation -- โข A Summation Formula and A Generalized Degree -- โข Structure and Dimension of Global Branches -- โข O-EPI Maps -- โข Dimension -- โข Application to Bifurcation Problems -- โข Equivariant Bifurcation -- โข Preliminaries -- โข Consequences of the Symmetry -- โข ?-EPI Maps -- โข ?-Degree -- โข The Equivariant J-Homomorphism and Sufficient Conditions -- โข Necessary and Sufficient Conditions for Equivariant Bifurcation -- โข Bibliography -- Critical Point Theory -- โข Introduction -- โข The Mountain Pass Theorem -- โข The Saddle Point Theorem -- โข Linking and A General Critical Point Theorem -- โข Periodic Solutions of Hamiltonian Systems -- โข Introduction -- โข The Technical Framework -- โข Periodic Solutions of Prescribed Energy -- โข Periodic Solutions of Prescribed Period -- โข Connecting Orbits -- โข Introduction -- โข Homoclinic Solutions -- โข Heteroclinic Solutions -- โข References -- Symplectic Topology: An Introduction -- โข The Classical Uncertainty Principle, Symplectic Rigidity -- โข Construction of Symplectic Invariants -- โข Generating Functions -- โข Historical Remarks -- โข Appendix: Rigidity for Finite Dimensional Lie Groups