Analysis and Topology in Nonlinear Differential Equations: A Tribute to Bernhard Ruf on the Occasion of his 60th Birthday

Description

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 Front Matter....Pages i-x Asymptotic Behavior of Sobolev Trace Embeddings in Expanding Domains....Pages 1-21 Multiplicity of Positive Solutions for an Obstacle Problem in ℝ....Pages 23-38 Multiplicity Results for some Perturbed and Unperturbed “Zero Mass” Elliptic Problems in Unbounded Cylinders....Pages 39-59 Basic Properties of Ultrafunctions....Pages 61-86 Multiple Radial Solutions at Resonance for Neumann Problems Involving the Mean Extrinsic Curvature Operator....Pages 87-101 Equivariant Bifurcation in Geometric Variational Problems....Pages 103-133 $$ W_0^{1,1} $$ Solutions in Some Borderline Cases of Elliptic Equations with Degenerate Coercivity....Pages 135-143 Remarks on p -Laplacian Problems Depending on the Gradient....Pages 145-161 Some Weighted Inequalities of Trudinger–Moser Type....Pages 163-174 Multiple Solutions for p -Laplacian Type Problems with an Asymptotically p -linear Term....Pages 175-186 Nonlocal Dynamic Problems with Singular Nonlinearities and Applications to MEMS....Pages 187-206 Existence and Multiplicity Results for Some Scalar Fields Equations....Pages 207-230 A Supercritical Elliptic Problem in a Cylindrical Shell....Pages 231-240 The Geometric Microlocal Analysis of Generalized Kimura and Heston Diffusions....Pages 241-266 On a Resonant Lane–Emden Problem....Pages 267-276 A Note on the Existence of a Positive Solution for a Non-autonomous Schrödinger–Poisson System....Pages 277-286 Low Energy Solutions for the Semiclassical Limit of Schrödinger–Maxwell Systems....Pages 287-300 An Abstract Theorem in Nonlinear Analysis....Pages 301-307 Existence and Nonexistence Results for a Schrödinger Equation with Saturable Nonlinearity....Pages 309-321 Bubble Concentration on Spheres for Supercritical Elliptic Problems....Pages 323-340 Normalized Solutions for a Schrödinger–Poisson System Under a Neumann Condition....Pages 341-352 On Singular Liouville Systems....Pages 353-385 Multiple Positive Solutions for a Nonsymmetric Elliptic Problem with Concave Convex Nonlinearity....Pages 387-403 Nonuniqueness for the Dirichlet Problem for Fully Nonlinear Elliptic Operators and the Ambrosetti–Prodi Phenomenon....Pages 405-421 Bifurcation at Isolated Eigenvalues for Some Elliptic Equations on ℝ N ....Pages 423-443 Geometric Aspects of Ambrosetti–Prodi Operators with Lipschitz Nonlinearities....Pages 445-456 The Backward $$ \lambda $$ -Lemma and Morse Filtrations....Pages 457-466