## Recent Trends in Nonlinear Analysis: Festschrift Dedicated to Alfonso Vignoli on the Occasion of His Sixtieth BirthdayAlfonso Vignoli, Jürgen Appell The book contains a collection of 21 original research papers which report on recent developments in various fields of nonlinear analysis. The collection covers a large variety of topics ranging from abstract fields such as algebraic topology, functional analysis, operator theory, spectral theory, analysis on manifolds, partial differential equations, boundary value problems, geometry of Banach spaces, measure theory, variational calculus, and integral equations, to more application-oriented fields like control theory, numerical analysis, mathematical physics, mathematical economy, and financial mathematics. The book is addressed to all specialists interested in nonlinear functional analysis and its applications, but also to postgraduate students who want to get in touch with this important field of modern analysis. It is dedicated to Alfonso Vignoli who has essentially contributed to the field, on the occasion of his sixtieth birthday. |

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### Contents

Alfonso Vignoli the Researcher Teacher and Friend | 1 |

How to Make Use of the Solution Set to Solve Boundary Value Problems | 15 |

On the Unique Solvability of Hammerstein Integral Equations with NonSymmetric Kernels | 27 |

The Invariance of Domain for C Fredholm Maps of Index Zero | 35 |

Positive Eigenfunctions for Some Unbounded Differential Operators | 41 |

Some Geometrical Properties of Rearrangement Invariant Spaces | 47 |

Strong Surjections and Nearness | 55 |

On the Vanishing Viscosity Approximation of a Time Dependent HamiltonJacobi Equation | 59 |

La valutazione di opzioni implicite nei mutui bancari | 117 |

Continuity of NearDuality Maps and Characterizations of Ideal Spaces of Measurable Functions | 139 |

A Spectral Theory for Semilinear Operators and its Applications | 149 |

Feedback Stability of Closed Sets for Nonlinear Control Systems | 165 |

Two Mechanical Systems and Equivariant Degree | 177 |

On the Semilinear Dirichlet Problem for a Class of Nonlocal Operators Generating Dirichlet Forms | 191 |

A Geometric Viewpoint | 205 |

Mountain Pass and Linking Type Solutions for Semilinear Dirichlet Forms | 217 |

Some Remarks on a Nonlinear Model of Competitive Equilibrium | 77 |

Almost Discrete Convergence | 83 |

Nonlinear Stability of Eigenvalues of Compact SelfAdjoint Operators | 93 |

A Bifurcation Theorem for Lagrangian Intersections | 105 |

SelfSimilar Measures in QuasiMetric Spaces | 233 |

C Fredholm Maps and Bifurcation for Quasilinear Elliptic Equations on IRA | 249 |

### Common terms and phrases

2000 Birkhauser Verlag Alfonso Anal assume assumption axiom of choice Banach spaces Birkhauser Verlag Basel/Switzerland boundary value problem bounded subsets closed compact subset condition consider continuous function contraction convergence convex convex set critical point defined definition dell'opzione denote differential equations dimensional Dirichlet forms Dirichlet problem dom(L eigenvalue equivariant exists finite fixed point Fredholm map Fredholm operator Hamiltonian Hence implies index zero integral intersection invariant Lagrangian submanifolds Lemma linear lower semicontinuous manifold map f MARTELLI Math measurable functions metric Moreover multivalued mutuo nonempty Nonlin nonlinear operators norm obtain opzioni Orlicz space orthogonal paper prezzo Proof properties Proposition prove quasi-distance quasi-metric space r.i. spaces Remark satisfied scadenza semilinear sequence solution set solvability spectral theory spectrum struttura subsolution subspace Suppose surjection tasso a breve tempo Theorem topology upper semicontinuous valore valutazione viscosity solution VlGNOLI volatilita ZABREJKO