Radial nonlinear elliptic problems with singular or vanishing potentials

In this paper we prove existence of radial solutions for the nonlinear elliptic problem $$-\mathrm{div}(A(|x|)\nabla u)+V(|x|)u=K(|x|)f(u) \quad \text{in }\mathbb{R}^{N},$$ \noindent with suitable hypotheses on the radial potentials $A,V,K$. We first get compact embeddings of radial weighted Sobolev spaces into sum of weighted Lebesgue spaces, and then we apply standard variational techniques to get existence results

Assessing the Impact of COVID-19 Prevention Measures on Adolescent Growth in Italy

COVID-19 infection has caused increased morbidity and mortality worldwide. Several strategies have been adopted around the world to prevent its spread. Italy underwent a long lockdown for face-to-face educational activities, which were replaced with online classes. This longitudinal study aimed to analyze the effects of COVID-19 prevention measures on physical growth and body image perception in a sample of Italian adolescents who experienced the pandemic-induced lockdown in 2020. In particular, we wished to ascertain how lifestyle changes had affected their growth rates and health. Special attention was paid to increases in adiposity indicators (BMI, waist circumference, waist-to-height ratio) and weight caused by reduced physical activity, and consequent possible dissatisfaction with body image. We assessed the impact of school closures by comparing the annual growth rate and body image perception changes of adolescents (n = 60; age = 11.3 & PLUSMN; 0.4 years) who experienced this isolation with those in the following years who did not experience these restrictions (n = 68; age = 11.4 & PLUSMN; 0.3 years). As a consequence of the lockdown, our results indicate a greater annual growth rate in weight and other indices of adiposity (p < 0.05). As the virus is continuing to evolve and propagate, larger population studies can verify and confirm our findings. In promoting health policy to prevent the ongoing prevalence of obesity in adolescents, an accurate assessment of whether the increase in obesity rates during the pandemic is to be considered a temporary trend is highly recommended