102,471 research outputs found
A Liouville theorem for elliptic equations with a potential on infinite graphs
No full textBiagi S, Meglioli G, Punzo F. A Liouville theorem for elliptic equations with a potential on infinite graphs. Calculus of Variations and Partial Differential Equations . 2024;63(7): 165.We investigate the validity of the Liouville property for a class of elliptic equations with a potential, posed on infinite graphs. Under suitable assumptions on the graph and on the potential, we prove that the unique bounded solution is u equivalent to 0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}. We also show that on a special class of graphs the condition on the potential is optimal, in the sense that if it fails, then there exist infinitely many bounded solutions
Young People and Nature: What Drives Underlying Behavioural Intentions towards Protected Areas Conservation?
No full textBlow-up and global existence for solutions to the porous medium equation with reaction and slowly decaying density
No full textWe study existence of global solutions and finite time blow-up of solutions to the Cauchy problem for the porous medium equation with a variable density ρ(x) and a power-like reaction term ρ(x)up with p>1; this is a mathematical model of a thermal evolution of a heated plasma (see [29]). The density decays slowly at infinity, in the sense that ρ(x)≲|x|−q as |x|→+∞ with q∈[0,2). We show that for large enough initial data, solutions blow-up in finite time for any p>1. On the other hand, if the initial datum is small enough and p>p ̄, for a suitable p ̄ depending on ρ,m,N, then global solutions exist. In addition, if p0 small enough, when m≤
A choice experiment on consumer perception of three generations of genetically modified foods
No full textBlow-up and global existence for the inhomogeneous porous medium equation with reaction
No full textWe study finite time blow-up and global existence of solutions to the Cauchy problem for the porous medium equation with a variable density ρ(x) and a power-like reaction term. We firstly consider the case that ρ(x) decays at infinity like the critical case [x]-2divided by a positive power of the logarithm of [x] and we show that for small enough initial data, solutions globally exist for any p > 1. On the other hand, when ρ(x) decays at infinity like the critical case [x]-2multiplied by a positive power of the logarithm of [x], if the initial datum is small enough, then one has global existence of the solution for any p > m, while if the initial datum is large enough, then the blow-up of the solutions occurs for any p > m. Such results generalize those established in [27] and [28], where it is supposed that ρ(x) decays at infinity like a power of [x], without logarithmic terms
UNIQUENESS FOR FRACTIONAL PARABOLIC AND ELLIPTIC EQUATIONS WITH DRIFT
No full textWe investigate uniqueness, in suitable weighted Lebesgue spaces, of solutions to a class of linear, nonlocal parabolic problems with a drift. More precisely, the problem is nonlocal due to the presence of the fractional Laplacian as diffusion operator. The drift term is driven by a smooth enough, possibly unbounded vector field b which satisfies a suitable growth condition in the set {x ∈ RN : > 0}. In general, our uniqueness class includes unbounded solutions; in particular, we get uniqueness of bounded solutions. Furthermore, we show sharpness of the hypothesis on the drift term b; in fact we show that, if the drift term b violates, in an appropriate sense, the mentioned growth condition (see (2.5)), then infinitely many bounded solutions to the problem exist. Finally, we also investigate uniqueness of a linear, nonlocal elliptic equation with a drift term obtaining similar results
Nutraceuticals: Some remarks by a choice experiment on food, health and new technologies
No full textNowadays people are increasingly interested in health foods, which are foods considered beneficial to well-being in ways that go beyond a normal healthy diet required for human nutrition. This study aims at providing a better understanding of the main factors leading to the purchase of a relatively new category of technological foods, namely nutraceuticals. Based on data collected on a sample of Italian families through a cross-sectional survey, which included choice experiment questions and socio-demographic characteristics, two specifications of discrete choice models allowed us to formalise the behavioural response linked to that purchase and to preference heterogeneity across consumers, and the willingness to pay for these products. Findings show that not all nutraceutical features are equally important in shaping consumers’ preferences for health-oriented foods. The role played by formal education in describing the behavioural response towards nutraceuticals and the significant preference heterogeneity across consumers in relation to specific nutraceutical features provide interesting insights to assist researchers and marketers in developing more market-oriented functional foods that gain consumer acceptance
On the Cauchy problem for a general fractional porous medium equation with variable density
No full textWe study the well-posedness of the Cauchy problem for a fractional porous medium equation with a varying density ρ>0. We establish existence of weak energy solutions; uniqueness and nonuniqueness is studied as well, according to the behavior of ρ at infinity. © 2013 Elsevier B.V. All rights reserved
Well-posedness for the cauchy problem for a fractional porous medium equation with variable density in one space dimension
No full textWe study the existence and uniqueness of the bounded solutions to a fractional nonlinear porous medium equation with a variable density in a one space dimension
- …
