Ebook: Nonlinear Functional Analysis and Its Applications

A NATO Advanced Study Institute on Nonlinear Functional Analysis and Its Applications was held in Hotel Villa del Mare, Maratea, It.a1y during April 22 - May 3, 1985. This volume consists of the Proceedings of the Institute. These Proceedings include the invited lectures and contributed papers given during the Institute. The papers have been refereed. The aim of these lectures was to bring together recent and up-to-date development of the subject, and to give directions for future research. The main topics covered include: degree and generalized degree theory, results related to Hamiltonian Systems, Fixed Point theory, linear and nonlinear Differential and Partial Differential Equations, Theory of Nielsen Numbers, and applications to Dynamical Systems, Bifurcation Theory, Hamiltonian Systems, Minimax Theory, Heat Equations, Pendulum Equation, Nonlinear Boundary Value Problems, and Dirichlet and Neumann problems for elliptic equations and the periodic Dirichlet problem for semilinear beam equations. I express my sincere thanks to Professors F. E. Browder, R. Conti, A. Do1d, D. E. Edmunds and J. Mawhin members of the Advisory Committee.

---

---

Content:
Front Matter....Pages i-xi
Cohomological Methods in Non-Free G-Spaces with Applications to General Borsuk-Ulam Theorems and Critical Point Theorems for Invariant Functionals....Pages 1-45
On a Theorem of Anosov on Nielsen Numbers for Nilmanifolds....Pages 47-53
Generalized Topological Degree and Bifurcation....Pages 55-73
Global Results on Continuation and Bifurcation for Equivariant Maps....Pages 75-111
Existence and Multiplicity for Semi-Linear Equations by the Duality Method....Pages 113-129
Special Problems Involving Uniqueness and Multiplicity in Hyperelasticity....Pages 131-145
An Index for Hamiltonian Systems with a Natural Order Structure....Pages 147-160
G. Darbo’s Fixed Point Principle After 30 Years....Pages 161-167
Best Approximation and Cones in Banach Spaces....Pages 169-176
Invariant Manifold Theorems with Applications....Pages 177-186
Some Applications of the Leray-Schauder Alternative to Differential Equations....Pages 187-194
Sequences of Iterates in Locally Convex Spaces....Pages 195-206
Periodic Solutions of Hamiltonian Systems: The Case of the Singular Potential....Pages 207-216
Oscillations et Analyse Non Lineaire: Proprietes Des Pulsations Des Solutions Periodiques (Cycles) De Certaines Equation Differentielles Autonomes Non Lineaires. Application De La Theorie DU Degre De Leray Schauder.....Pages 217-221
A Fixed Point Theorem for Two Commuting Mappings....Pages 223-227
Nonlinear Elliptic Problems Involving Critical Sobolev Exponent in the Case of Symmetrical Domains....Pages 229-233
Periodic Solutions of Pendulum Like Third Order Differential Equations....Pages 235-239
Double Resonance at the First and Second Eigenvalues for the Nonlinear Heat Equation....Pages 241-252
Generalised Riemann Invariants....Pages 253-276
Unbounded Perturbations of Forced Harmonic Oscillations at Resonance....Pages 277-289
Minimizing the Number of Fixed Points....Pages 291-297
Approximate Fixed Points for Mappings in Banach Spaces....Pages 299-303
Invariantly Complemented Subspaces and Groups with Fixed Point Property....Pages 305-311
On A Certain Difference-Differential Equation....Pages 313-316
Limit Cycles of Certain Polynomial Systems....Pages 317-326
Convexity Structures and Kannan Maps....Pages 327-333
On Some Converses of Generalized Banach Contraction Principles....Pages 335-351
Multiplicity Results for Superlinear Elliptic Equations....Pages 353-367
A Note on Periodic Solutions of Heat Equation with a Superlinear Term....Pages 369-374
Fixed Point Sets on Pairs of Spaces....Pages 375-386
Fixed Point Free Deformations on Compact Polyhedra....Pages 387-392
Minimax Principles for a Class of Lower Semicontinuous Functions and Applications to Nonlinear Boundary Value Problems....Pages 393-399
Fixed Point Theorems and Coincidence Theorems for Upper Hemi-Continuous Mappings....Pages 401-408
Back Matter....Pages 409-418

---

Content:
Front Matter....Pages i-xi
Cohomological Methods in Non-Free G-Spaces with Applications to General Borsuk-Ulam Theorems and Critical Point Theorems for Invariant Functionals....Pages 1-45
On a Theorem of Anosov on Nielsen Numbers for Nilmanifolds....Pages 47-53
Generalized Topological Degree and Bifurcation....Pages 55-73
Global Results on Continuation and Bifurcation for Equivariant Maps....Pages 75-111
Existence and Multiplicity for Semi-Linear Equations by the Duality Method....Pages 113-129
Special Problems Involving Uniqueness and Multiplicity in Hyperelasticity....Pages 131-145
An Index for Hamiltonian Systems with a Natural Order Structure....Pages 147-160
G. Darbo’s Fixed Point Principle After 30 Years....Pages 161-167
Best Approximation and Cones in Banach Spaces....Pages 169-176
Invariant Manifold Theorems with Applications....Pages 177-186
Some Applications of the Leray-Schauder Alternative to Differential Equations....Pages 187-194
Sequences of Iterates in Locally Convex Spaces....Pages 195-206
Periodic Solutions of Hamiltonian Systems: The Case of the Singular Potential....Pages 207-216
Oscillations et Analyse Non Lineaire: Proprietes Des Pulsations Des Solutions Periodiques (Cycles) De Certaines Equation Differentielles Autonomes Non Lineaires. Application De La Theorie DU Degre De Leray Schauder.....Pages 217-221
A Fixed Point Theorem for Two Commuting Mappings....Pages 223-227
Nonlinear Elliptic Problems Involving Critical Sobolev Exponent in the Case of Symmetrical Domains....Pages 229-233
Periodic Solutions of Pendulum Like Third Order Differential Equations....Pages 235-239
Double Resonance at the First and Second Eigenvalues for the Nonlinear Heat Equation....Pages 241-252
Generalised Riemann Invariants....Pages 253-276
Unbounded Perturbations of Forced Harmonic Oscillations at Resonance....Pages 277-289
Minimizing the Number of Fixed Points....Pages 291-297
Approximate Fixed Points for Mappings in Banach Spaces....Pages 299-303
Invariantly Complemented Subspaces and Groups with Fixed Point Property....Pages 305-311
On A Certain Difference-Differential Equation....Pages 313-316
Limit Cycles of Certain Polynomial Systems....Pages 317-326
Convexity Structures and Kannan Maps....Pages 327-333
On Some Converses of Generalized Banach Contraction Principles....Pages 335-351
Multiplicity Results for Superlinear Elliptic Equations....Pages 353-367
A Note on Periodic Solutions of Heat Equation with a Superlinear Term....Pages 369-374
Fixed Point Sets on Pairs of Spaces....Pages 375-386
Fixed Point Free Deformations on Compact Polyhedra....Pages 387-392
Minimax Principles for a Class of Lower Semicontinuous Functions and Applications to Nonlinear Boundary Value Problems....Pages 393-399
Fixed Point Theorems and Coincidence Theorems for Upper Hemi-Continuous Mappings....Pages 401-408
Back Matter....Pages 409-418
....