Multiple solutions for a class of degenerate nonlocal problems involving sublinear nonlinearities

In this article, we use the three critical points theorem by G. Bonanno [3] in order to investigate the multiplicity of solutions for some nonlocal degenerate problems

Interdependent binary choices under social influence: phase diagram for homogeneous unbiased populations

Coupled Ising models are studied in a discrete choice theory framework, where they can be understood to represent interdependent choice making processes for homogeneous populations under social influence. Two different coupling schemes are considered. The nonlocal or group interdependence model is used to study two interrelated groups making the same binary choice. The local or individual interdependence model represents a single group where agents make two binary choices which depend on each other. For both models, phase diagrams, and their implications in socioeconomic contexts, are described and compared in the absence of private deterministic utilities (zero opinion fields).Comment: 17 pages, 3 figures. This is the pre-peer reviewed version of the following article: Ana Fern\'andez del R\'io, Elka Korutcheva and Javier de la Rubia, Interdependent binary choices under social influence, Wiley's Complexity, 2012; which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/cplx.21397/abstrac

Surface-plasmon resonances of arbitrarily shaped nanometallic structures in the small-screening-length limit

According to the hydrodynamic Drude model, surface-plasmon resonances of metallic nanostructures blueshift owing to the nonlocal response of the metal's electron gas. The screening length characterising the nonlocal effect is often small relative to the overall dimensions of the metallic structure, which enables us to derive a coarse-grained nonlocal description using matched asymptotic expansions; a perturbation theory for the blueshifts of arbitrary shaped nanometallic structures is then developed. The effect of nonlocality is not always a perturbation and we present a detailed analysis of the "bonding" modes of a dimer of nearly touching nanowires where the leading-order eigenfrequencies and eigenmode distributions are shown to be a renormalisation of those predicted assuming a local metal permittivity