Spectral theory and nonlinear analysis with applications to spatial ecology Universidad Complutense de Madrid, Spain, 14-15 June 2004 (World Scientific, 2005)
On the positive solutions of the logistic weighted elliptic BVP with sublinear mixed boundary conditions -- Logarithmic interpolation spaces -- Remarks on large solutions -- Well posedness and asymptotic behaviour of a closed loop thermosyphon -- Uniqueness of large solutions for a class of radially symmetric elliptic equations -- Cooperation and competition, strategic alliances, and the cambrian explosion -- Local smith form and equivalence for one-parameter families of F'redholm operators of index zero -- Multilump solutions of the non-linear Schrodinger equation -- a scaling approach -- Some elliptic problems with nonlinear boundary conditions -- Dynamical systems method (DSM) and nonlinear problems -- Some recent results on periodic, jumping nonlinearity problems -- Some remarks about the cubic Schrodinger equation on the line -- Some remarks on the invariance of level sets in dynamical systems
Annotation 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 Schr?dinger 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