3,128 research outputs found
On the spectrum of a nonlinear planar problem
No full textWe consider the eigenvalue problem
-Δυ = λμeuλυ ---in Ω,
||υ||∞ = 1------------------------------------(0.1)
υ = 0 ------------on ∂Ω,
where Ω is a bounded smooth domain of R2, λ>0 is a real parameter and uλ is a solution of
-Δuλ = λeuλ-----in Ω,
uλ = 0-----------on ∂Ω
such that λ∫Ω euλ →8π as λ→0. In this paper we study the asymptotic behavior of the eigenvalues μ of (0.1) as λ→0. Moreover some explicit estimates for the four first eigenvalues and eigenfunctions are given.
Other related results as the Morse index of the solution uλ will be proved
Strict convexity of level sets of solutions of some nonlinear elliptic equations
No full textIn this paper we study the convexity of the level sets of solutions of the problem where f is a suitable function with subcritical or critical growth. Under some assumptions on the Gauss curvature of ∂Ω, we prove that the level sets of the solution of (0.1) are strictly convex
Evaluation of a combined sediment yield and solid transport system in a small alpine catchment
No full text
Linear perturbations for the critical Hénon problem
No full textIn this paper, we study the problem −∆u = |x| α u p α + |x| β u in Ω u> 0 in Ω u =0 on ∂Ω, (0.1) , Ω is a smooth bounded domain of R N with 0 ∈ Ω where p α = N +2+2α N −2 and N ≥ 4. We show that, for α ≥ 0 and 0 ≤ β ≤ N − 4, there exists one solution concentrating at x = 0 as → 0. Moreover, we prove that,
if Ω is a ball, there exist no radial solution if α = β > N − 4
Water Soil Erosion Evaluation in a Small Alpine Catchment Located in Northern Italy: Potential Effects of Climate Change
No full textWater erosion and evaluation of the average annual soil loss considering the potential effects of climate change are the focus of this study, based on the application of two empirical models, the RUSLE (Revised Universal Soil Loss Equation) and the EPM (Erosion Potential Method), to an Italian case study. A small mountain basin, the Guerna creek watershed, is located in the Central Southern Alps (Lombardy, Southern Alps, Bergamo), and it has been affected in the past by flooding and erosion events, which stressed the hydraulic weaknesses of the study area. Three different future climate scenarios were built for the middle of this century (from 2041 to 2060) on the basis of CORDEX data and Representative Concentration Pathways (RCP) set by the IPCC (Intergovernmental Panel on Climate Change) future scenarios: RCP 2.6, RCP 4.5, and RCP 8.5. As concerns climate, precipitation and air temperature are the variables used in the empirical models. On the other hand, potential effects on land use were also considered. Computed soil loss of 87 t/ha/year and 29.3 t/ha/year was achieved using the RUSLE equation and EPM method respectively, without considering the potential effects of climate change. The results achieved showed that climate change impacts on water erosion may not be negligible even by the middle of the current century (the annual average soil loss could change by 6–10% on a basin scale), and a major role is being played by seasonality in rainfall peak intensity
Supercritical elliptic problem with nonautonomous nonlinearities
No full textIn this paper we study the problem
[...] where pα = N+2+2α / N−2 , Ω is a smooth bounded domain of RN, 0 ∈ Ω, N [...]3 and α∈(0, 1]. We show that, for ∈ small enough, there exists at least one solution concentrating at x= 0
- …
