Topological Nonlinear Analysis -

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Sommaire:
Variational Methods and Nonlinear Problems: Classical Results and Recent Advances.- ? Introduction.- ? Lusternik-Schnirelman Theory.- ? Applications to Nonlinear Eigenvalues.- ? Unbounded Functionals.- ? Elliptic Dirichlet Problems.- ? Singular Potentials.- ? References.- to Morse Theory: A New Approach.- ? Introduction.- ? Contents.- ? The Abstract Theory.- ? The Morse Index.- ? The Poincar? Polynomial.- ? The Conley Blocks.- ? The Morse Relations.- ? Morse Theory for Degenerate Critical Points.- ? Some Existence Theorems.- ? An Application to Riemannian Geometry.- ? Riemannian Manifolds.- ? Geodesies.- ? The Morse Theory for Geodesics.- ? The Index Theorem.- ? An Application to Space-Time Geometry.- ? Introduction.- ? Some Examples of Lorentzian Manifolds.- ? Morse Theory for Lorentzian Manifolds.- ? Preliminary Lemmas.- ? Proof of The Morse Relations For Static Space-Time.- ? Some Application to a Semilinear Elliptic Equation.- ? Introduction.- ? The Sublinear Case.- ? The Superlinear Case Morse Relations for Positive Solutions.- ? The Functional Setting.- ? Some Hard Analysis.- ? The Photography Method.- ? The Topology of The Strip.- ? References.- Applications of Singularity Theory to the Solutions of Nonlinear Equations.- ? The Full Lyapunov-Schmidt Reduction.- ? Mather's Theory of C?-Stability of Mappings - Global Theory.- ? Mather's Local Theory as Paradigm.- ? Singularity Theory with Special Conditions.- ? The Structure of Nonlinear Fredholm Operators.- ? Multiplicities of Solutions to Nonlinear Equations.- ? The Theory for Topological Equivalence.- ? Bibliography.- Fixed Point Index Calculations and Applications.- ? The Fixed Point Index.- ? Some Remarks onConvex Sets.- ? A Basic Index Calculation.- ? Index Calculations in Product Cones.- ? Applications of Index Formulae - I.- ? Applications of Index Formulae - II.- ? Some Global Branches.- ? Monotone Dynamical Systems.- ? Preliminaries.- ? Connecting Orbits and Related Results.- ? Generic Convergence.- ? References.- Topological Bifurcation.- ? Abstract.- ? Introduction.- ? Preliminaries.- ? One Parameter Bifurcation.- ? Local Bifurcation.- ? Global Bifurcation.- ? Special Nonlinearities.- ? Multiparameter Bifurcation.- ? Sufficient Conditions for Local Bifurcation.- ? Necessary Conditions for Linearized Local Bifurcation.- ? Multiparameter Global Bifurcation.- ? A Summation Formula and A Generalized Degree.- ? Structure and Dimension of Global Branches.- ? O-EPI Maps.- ? Dimension.- ? Application to Bifurcation Problems.- ? Equivariant Bifurcation.- ? Preliminaries.- ? Consequences of the Symmetry.- ? ?-EPI Maps.- ? ?-Degree.- ? The Equivariant J-Homomorphism and Sufficient Conditions.- ? Necessary and Sufficient Conditions for Equivariant Bifurcation.- ? Bibliography.- Critical Point Theory.- ? Introduction.- ? The Mountain Pass Theorem.- ? The Saddle Point Theorem.- ? Linking and A General Critical Point Theorem.- ? Periodic Solutions of Hamiltonian Systems.- ? Introduction.- ? The Technical Framework.- ? Periodic Solutions of Prescribed Energy.- ? Periodic Solutions of Prescribed Period.- ? Connecting Orbits.- ? Introduction.- ? Homoclinic Solutions.- ? Heteroclinic Solutions.- ? References.- Symplectic Topology: An Introduction.- ? The Classical Uncertainty Principle, Symplectic Rigidity.- ? Construction of Symplectic Invariants.- ? Generating Functions.- ?Historical Remarks.- ? Appendix: Rigidity for Finite Dimensional Lie Groups.