Solvabilty of generalized Hammerstein integral equations on unbounded domains, with sign-changing kernels

In this work we study an Hammerstein generalized integral equation u(t)=∫_{-∞}^{+∞}k(t,s) f(s,u(s),u′(s),...,u^{(m)}(s))ds, where k:ℝ²→ℝ is a W^{m,∞}(ℝ²), m∈ℕ, kernel function and f:ℝ^{m+2}→ℝ is a L¹-Carathéodory function. To the best of our knowledge, this paper is the first one to consider discontinuous nonlinearities with derivatives dependence, without monotone or asymptotic assumptions, on the whole real line. Our method is applied to a fourth order nonlinear boundary value problem, which models moderately large deflections of infinite nonlinear beams resting on elastic foundations under localized external loads.

Annual Average Value of Solar Radiation and its Variability in Portugal

Solar resource assessment is essential for the different phases of solar energy projects, such as preliminary design engineering, financing including due diligence and, later, insurance phases. An important aspect is the long term resource estimation. This kind of estimation can only be obtained through the statistical analysis of long-term data series of solar radiation measurements, preferably ground measurements. This paper is a first step in this direction, with an initial statistical analysis performed over the radiation data from a national measurement network, consisting of eighty-nine meteorological stations. These preliminary results are presented in figures that represent the annual average values of Global Horizontal Irradiation (GHI) and its Variability in the Portuguese continental territory. These results show that the South of Portugal is the most suitable area for the implementation of medium to large scale solar plants.