## Nonlinear functional analysis and its applications, Part 1 (Google eBook) |

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### Contents

1 | |

7 | |

Parabolic Evolution Equations with Nonlinear Boundary Conditions | 17 |

Nonlinear Oscillations with Minimal Period | 29 |

On Steady NavierStokes Flow Past a Body in the Plane | 37 |

On a Contraction Theorem and Applications | 51 |

Dual Variational Principles for Eigenvalue Problems | 55 |

Generalized Elliptic Solutions of the Dirichlet Problem for nDimensional MongeAmpère Equations | 73 |

A Global Fixed Point Theorem for Symplectic Maps and Subharmonic Solutions of Hamiltonian Equations on Tori | 283 |

Harmonic Maps from the Disk into the Euclidean NSphere | 301 |

Nonlinear Semigroups and Evolution Governed by Accretive Operators | 305 |

A Theorem of Mather and the Local Structure of Nonlinear Fredholm Maps | 339 |

Remarks on S1 Symmetries and a Special Degree for S1Invariant Gradient Mappings | 353 |

Abstract Differential Equations Maximal Regularity and Linearization | 359 |

Positive Solutions for Some Classes of Semilinear Elliptic Problems | 371 |

The Boundary of the Support of the Solutions | 381 |

Existence and Containment of Solutions to Parabolic Systems | 103 |

Periodic Hamiltonian Trajectories on Starshaped Manifolds | 109 |

Integrability of Nonlinear Differential Equations via Functional Analysis | 117 |

Extinction of the Solutions of Some Quasilinear Elliptic Problems of Arbitrary Order | 125 |

On a System of Degenerate Diffusion Equations | 133 |

Pointwise Continuity for a Weak Solution of a Parabolic Obstacle Problem | 141 |

A Note on Iteration for Pseudoparabolic Equations of Fissured Media Type | 147 |

Homogenization of TwoPhase Flow Equations | 157 |

Some Variational Problems with Lack of Compactness | 165 |

Degree Theory for Nonlinear Mappings | 203 |

Construction of Periodic Solutions of Periodic Contractive Evolution Systems from Bounded Solutions | 227 |

An Abstract Critical Point Theorem for Strongly Indefinite Functionals | 237 |

Uniqueness of Positive Solutions for a Sublinear Dirichlet Problem | 243 |

Applications of Homology Theory to Some Problems in Differential Equations | 253 |

On the Continuation Method and the Method of Monotone Iterations | 263 |

Existence Theorems for Superlinear Elliptic Dirichlet Problems in Exterior Domains | 271 |

An Index Theory for Periodic Solutions of Convex Hamiltonian Systems | 395 |

An Extension of the LeraySchauder Degree for Fully Nonlinear Elliptic Problems | 425 |

Nonlinear Spectral Manifolds for the NavierStokes Equations | 439 |

Regularity Criteria for Weak Solutions of the NavierStokes System | 449 |

A Strongly Nonlinear Elliptic Problem in OrliczSobolev Spaces | 455 |

Nontrivial Solutions of Semilinear Elliptic Equations of Fourth Order | 463 |

Approximation in Sobolev Spaces and Nonlinear Potential Theory | 473 |

Some Free Boundary Problems for PredatorPrey Systems with Nonlinear Diffusion | 481 |

On Positive Solutions of Semilinear PeriodicParabolic Problems | 489 |

The Topological Degree at a Critical Point of MountainPass Type | 501 |

On a Conjecture of Lohwater About Asymptotic Values of Meromorphic Functions | 511 |

Parametrix of b | 521 |

Applications of NashMoser Theory to Nonlinear Cauchy Problems | 525 |

Structure and Topological Dimension of Global Branches of Solutions | 529 |

### Common terms and phrases

1980 Mathematics Subject accretive Amer Anal applications approximation assume assumptions asymptotic Banach space bifurcation boundary conditions boundary value problems compact consider const constant continuous convex functions corresponding critical points defined definition degree function degree theory denote Dirichlet problem eigenfunction eigenvalue problem elliptic equations equivalent estimate exists finite fixed point Floquet multipliers follows Fredholm given global Hamiltonian system Hence Hilbert space holds homotopy implies inequality infimum integral invariant Lemma Leray-Schauder linear operator m-accretive manifold Math Mathematics Subject Classification maximum principle mild solution minimal Monge-Ampere equations monotone Moreover Navier-Stokes Navier-Stokes equations nonlinear elliptic nontrivial norm obtain parabolic partial differential equations periodic solutions perturbation positive solutions proof of Theorem properties PROPOSITION prove Pure Appl quasilinear REMARK resp satisfies semigroup semilinear sequence smooth Sobolev spaces Suppose topological trajectories unique vector fields Volume 45 weak solution x e fl zero