This volume details some of the latest advances in spectral theory and nonlinear analysis through various cutting-edge theories on algebraic multiplicities, global bifurcation theory, non-linear Schrödinger equations, non-linear boundary value problems, large solutions, metasolutions, dynamical systems, and applications to spatial ecology.The main scope of the book is bringing together a series of topics that have evolved separately during the last decades around the common denominator of spectral theory and nonlinear analysis — from the most abstract developments up to the most concrete applications to population dynamics and socio-biology — in an effort to fill the existing gaps between these fields.Contents:On the Positive Solutions of the Logistic Weighted Elliptic BVP with Sublinear Mixed Boundary Conditions (S Cano-Casanova)Logarithmic Interpolation Spaces (F Cobos)Remarks on Large Solutions (J Carcía-Melián & J S de Lis)Well Posedness and Asymptotic Behavior of a Closed Loop Thermosyphon (A Jiménez-Casas)Uniqueness of Large Solutions for a Class of Radially Symmetric Elliptic Equations (J López-Gómez)Cooperation and Competition, Strategic Alliances, and the Cambrian Explosion (J López-Gómez & M Molina-Meyer)Local Smith Form and Equivalence for One-Parameter Families of Fredholm Operators of Index Zero (J López-Gómez & C Mora-Corral)Multilump Solutions of the Nonlinear Schrödinger Equations — A Scaling Approach (R J Magnus)Some Elliptic Problems with Nonlinear Boundary Conditions (C Morales-Rodrigo & A Suárez)Dynamical System Method (DSM) and Nonlinear Problems (A G Ramm)Some Recent Results on Periodic, Jumping Nonlinearity Problems (B P Rynne)Some Remarks about the Cubic Schrödinger Equation on the Line (L Vega)Some Remarks on the Invariance of Level Sets in Dynamical Systems (J M Vegas)Readership: Nonlinear scientists and mathematicians.