Contents -- Preface -- Poster of the Seminar -- On the Positive Solutions of the Logistic Weighted Elliptic BVP with Sublinear Mixed Boundary Conditions S. Cano-Casanova -- 1. Introduction -- 2. Preliminaries, Definitions and Main Notations -- 3. On the Uniqueness and Regularity of Positive Solutions of Problem ( 1 ) ~ -- 4. On the Existence of Positive Solutions of Problem (1) -- Acknowledgments -- References -- Logarithmic Interpolation Spaces F. Cobos -- 1. Introduction -- 2. Function Spaces -- 3. Abstract Logarithmic Interpolation Spaces -- 4. Concrete Logarithmic Interpolation Spaces -- References -- Remarks on Large Solutions J. Garcia-Melian and J. Sabina de Lis -- 1. Introduction -- 2. Preliminaries -- 3. Contact null set-boundary -- 4. Inner null set -- 5. A normal derivative estimate -- Acknowledgments -- References -- Well Posedness and Asymptotic Behaviour of a Closed Loop Thermosyphon A . Jimenez-Casas -- 1. Introduction -- 2. Well posedness, existence and uniqueness of solutions -- 2.1. Well posedness. Discussion about the suitable framework -- 2.2. Existence and uniqueness of solutions -- 3. Asymptotic behaviour for solutions under orthogonality condition -- 3.1. Previous results and notations -- 3.2. Asymptotic behaviour -- 3.3. Concluding remarks -- Acknowledgments -- References -- Uniqueness of Large Solutions for a Class of Radially Symmetric Elliptic Equations J. Ldpez-Gdmez -- 1. Introduction -- 2. Proof of Theorem 1.1 -- 3. A pivotal one-dimensional problem -- 3.1. Existence and uniqueness -- 3.2. Global lower estimates for l( t ) -- 3.3. Global properties of the function F( t ) -- 3.4. Global estimates of l( t ) in terms of F (t) -- 3.5. The blow-up rate of l ( t ) at t = 0 -- 4. Boundary blow-up rate of the large solution -- References.

Cooperation and Competition, Strategic Alliances, and the Cambrian Explosion J. Lopez-Gomez and M. Molina-Meyer -- 1. Introduction -- 2. The Cambrian explosion -- 3. Cooperation and competition in Ecology -- 4. Cooperation and competition in Management -- 5. The importance of mathematical models -- 6. Modeling cooperation in competitive environments -- 7. The balance of cooperation and competition -- 8. Searching for general principles in co-opetition theory -- References -- Local Smith Form and Equivalence for One-parameter Families of Fredholm Operators of Index Zero J. Lopez-Gomez and M. Mora-Corral -- 1. Introduction -- 2. Jordan chains and canonical sets -- 3. Local Smith form -- 4. Transversal eigenvalues -- 5. Algebraic eigenvalues and transversalization -- 6. Canonical sets at transversal eigenvalues -- 7. Characterization of the existence of the local Smith form -- 8. Equivalence of families -- References -- Multilump Solutions of the Non-linear Schrodinger Equation - A Scaling Approach R. J. Magnus -- 1. Statement of the problem -- 2. Background -- 3. Method of scaling -- 4. Solution of the limiting equation -- 5. Multi-bump solutions -- 6. Passage to the limit equation -- Implicit function theorem -- Make the assumptions: -- Modified implicit function theorem -- Make the assumptions: -- 7. Study of the rescaled equations -- References -- Some Elliptic Problems with Nonlinear Boundary Conditions C. Morales-Rodrigo and A . Suarez -- 1. Introduction -- 2. Some Preliminary Results: Eigenvalues Problems -- 3. Bifurcation Results for Equations with Nonlinear Boundary -- 4. Stability, Uniqueness and a-priori Bounds -- 5. Some Applications -- 5.1. Elliptic equation with a logistic term at the boundary -- 5.2. A sublinear-superlinear equation -- 5.3. The concave-convex equation -- References.

Dynamical Systems Method (DSM) and Nonlinear Problems A . G. Ramm -- 1. Introduction -- 2. Well-posed problems -- 3. Surjectivity of F -- 4. When is F a global homeomorphism? -- 5. Linear ill-posed equations -- 6. Nonlinear equations with monotone operators -- 7. A differential inequality -- 8. A spectral assumption and nonlinear equations -- 9. A singular perturbation problem -- 10. Nonsmooth monotone operators -- 11. Unbounded operators -- 12. Equations in Banach spaces -- 13. Iterative processes for well-posed problems -- 14. Iterative process for ill-posed problems with monotone operators -- 15. Newton-type methods without inverting the derivative -- 16. Equations with non-monotone operators -- References -- Some Recent Results on Periodic, Jumping Nonlinearity Problems B. P. Rynne -- 1. Introduction -- 2. Notation -- 3. Half-eigenvalues -- 4. Multiplicity results -- 5. Solvability properties -- 6. The Fucik spectrum -- 6.1. The separated case -- 6.2. The periodic case -- References -- Some Remarks about the Cubic Schrodinger Equation on the Line L. Vega -- 1. Introduction -- 2. Some Physical Models -- 3. Conservation Laws -- 4. Symmetries -- 5. Stability -- References -- Some Remarks on the Invariance of Level Sets in Dynamical Systems J. M. Vegas -- 1. Introduction -- 2. Statement of the problem -- 2.1. The main theorem -- 2.2. A n application (first part) -- 3. Nondifferentiable Liapunov functions -- 3.1. A n application (second part ) -- 3.2. Desingularization -- 4. Higher-order derivatives -- References.