## Analysis and Topology in Nonlinear Differential Equations: A Tribute to Bernhard Ruf on the Occasion of his 60th BirthdayDjairo G de Figueiredo, João Marcos do Ó, Carlos Tomei This volume is a collection of articles presented at the Workshop for Nonlinear Analysis held in João Pessoa, Brazil, in September 2012. The influence of Bernhard Ruf, to whom this volume is dedicated on the occasion of his 60th birthday, is perceptible throughout the collection by the choice of themes and techniques. The many contributors consider modern topics in the calculus of variations, topological methods and regularity analysis, together with novel applications of partial differential equations. In keeping with the tradition of the workshop, emphasis is given to elliptic operators inserted in different contexts, both theoretical and applied. Topics include semi-linear and fully nonlinear equations and systems with different nonlinearities, at sub- and supercritical exponents, with spectral interactions of Ambrosetti-Prodi type. Also treated are analytic aspects as well as applications such as diffusion problems in mathematical genetics and finance and evolution equations related to electromechanical devices. |

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### Contents

1 | |

Multiplicity of Positive Solutions for an Obstacle Problem in R | 23 |

Multiplicity Results for some Perturbed and Unperturbed Zero Mass Elliptic Problems in Unbounded Cylinders | 39 |

Basic Properties of Ultrafunctions | 60 |

Multiple Radial Solutions at Resonance for Neumann Problems Involving the Mean Extrinsic Curvature Operator | 87 |

Equivariant Bifurcation in Geometric Variational Problems | 103 |

W0 11 Solutions in Some Borderline Cases of Elliptic Equations with Degenerate Coercivity | 134 |

Remarks on pLaplacian Problems Depending on the Gradient | 145 |

On a Resonant LaneEmden Problem | 267 |

A Note on the Existence of a Positive Solution for a Nonautonomous SchrödingerPoisson System
| 277 |

Low Energy Solutions for the Semiclassical Limit of SchrödingerMaxwell Systems | 287 |

An Abstract Theorem in Nonlinear Analysis | 301 |

Existence and Nonexistence Results for a Schrödinger Equation with Saturable Nonlinearity
| 309 |

Bubble Concentration on Spheres for Supercritical Elliptic Problems | 322 |

Normalized Solutions for a SchrödingerPoisson System Under a Neumann Condition | 341 |

On Singular Liouville Systems | 353 |

Some Weighted Inequalities of TrudingerMoser Type | 162 |

Multiple Solutions for pLaplacian Type Problems with an Asymptotically plinear Term | 175 |

Nonlocal Dynamic Problems with Singular Nonlinearities and Applications to MEMS | 187 |

Existence and Multiplicity Results for Some Scalar Fields Equations | 207 |

A Supercritical Elliptic Problem in a Cylindrical Shell | 231 |

The Geometric Microlocal Analysis of Generalized Kimura and Heston Diffusions | 241 |

Multiple Positive Solutions for a Nonsymmetric Elliptic Problem with Concave Convex Nonlinearity | 387 |

Nonuniqueness for the Dirichlet Problem for Fully Nonlinear Elliptic Operators and the AmbrosettiProdi Phenomenon | 404 |

Bifurcation at Isolated Eigenvalues for Some Elliptic Equations on RN | 423 |

Geometric Aspects of AmbrosettiProdi Operators with Lipschitz Nonlinearities | 444 |

The Backward λLemma and Morse Filtrations | 457 |

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2014 Springer International apply argument assume assumption asymptotic Banach manifold Banach space bifurcation boundary conditions bounded compact consider converges convex critical points deﬁned deﬁnition denote Dirichlet problem domain eigenfunction eigenvalue elliptic equations elliptic problems estimate exists ﬁnd ﬁnite ﬁrst ﬁxed function heat kernel Hence holds implies inequality inﬁnitely International Publishing Switzerland Lemma linear Lipschitz manifold Math Mathematics Mathematics Subject Classification mean curvature Moreover Morse index Mountain Pass Theorem multiplicity results Neumann problem nonlinear Nonlinear Anal nonlinear elliptic norm obtain operator p-Laplacian parametrix positive solutions proof of Theorem properties Proposition 2.1 prove radial solutions Remark satisﬁes satisfying sequence singular smooth Sobolev Sobolev space Springer International Publishing subset subspace sufﬁciently supersolution symmetric Theorem 1.1 theory topological ultrafunctions uniformly unique variational vector weak solutions