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We study the asymptotic behavior of radially symmetric solutions to the subcritical semilinear elliptic problem $$\displaylines{ -\Delta u = u^{\frac{N+2}{N-2}}/[\log(e+u)]^{\alpha}\quad \text{in } \Omega=B_R(0)\subset\mathbb{R}^N,\cr u>0,\quad \text{in } \Omega,\cr u=0,\quad \text{on } \partial \Omega, }$$ as $\alpha\to 0^+$. Using asymptotic estimates, we prove that there exists an explicitly defined constant L(N,R)>0, only depending on N and R, such that $$ \limsup_{\alpha\to0^+} \frac{\alpha u_\alpha (0)^2} {[\log(e+u_\alpha (0))]^{1+\frac{\alpha(N+2)}{2}}} \leq L(N,R) \le 2^*\liminf_{\alpha\to0^+}\frac{\alpha u_\alpha (0)^2} {[\log(e+u_\alpha (0))]^{\frac{\alpha(N-4)}2}}. $$

Objective The Latin American Network of Congenital Malformations: ReLAMC was established in 2017 to provide accurate congenital anomaly surveillance. This study used data from ReLAMC registries to quantify the prevalence of microcephaly from 2010 to 2017 (before, during and after the Zika virus epidemic).Design Nine ReLAMC congenital anomaly registries provided case-level data or aggregate data for any live births, still births or terminations of pregnancy with microcephaly. Births to pregnant women infected with Zika virus first occurred in Brazil in 2015, and in the remaining registry areas in 2016 with the exception of Chile that did not experience Zika virus. Therefore the prevalence of microcephaly for 2010–2014 and individual years 2015, 2016 and 2017 was estimated using multilevel random effect Poisson models. Clinical classification and characteristics of the cases were compared pre and post Zika for all centres providing individual case-level data.Results The prevalence of microcephaly for all registries excluding Brazil was 2.3 per 10 000 (95% CI 2.0 to 2.6) for 2010–2014 rising to 5.4 (95% CI 4.8 to 6.0) in 2016 and 5.9 (95% CI 5.3 to 6.6) in 2017. Brazil had a prevalence of 0.6 per 10 000 (95% CI 0.5 to 0.6) in 2010–2014, rising to 5.8 (95% CI 5.6 to 6.1) in 2015, 8.0 (95% CI 7.6 to 8.3) in 2016 and then falling in 2017. Only 29 out of 687 cases of microcephaly were reported as congenital Zika syndrome in countries excluding Brazil.Conclusions The prevalence of microcephaly was influenced both by Zika causing congenital Zika syndrome and by increased reporting awareness.

Purpose The Mother and Child COVID-19 study is a cohort recruiting pregnant women and their children in Cantabria, North of Spain, during COVID-19 pandemic in order to ascertain consequences of SARS-CoV-2 infection on pregnant women and their descendants. This article reports the cohort profile and preliminary results as recruitment is still open.Participants Three subcohorts can be identified at recruitment. Subcohort 1 includes women giving birth between 23 March and 25 May 2020; they have been retrospectively recruited and could have been exposed to COVID-19 only in their third trimester of pregnancy. Subcohort 2 includes women giving birth from 26 May 2020 on; they are being prospectively recruited and could have been exposed to COVID-19 in both their second and third trimesters of pregnancy. Subcohort 3 includes women in their 12 week of pregnancy prospectively recruited from 26 May 2020 on; they could have been exposed to COVID-19 anytime in their pregnancy. All women are being tested for SARS-CoV-2 infection using both RT-PCR for RNA detection and ELISA for anti-SARS-CoV-2 antibodies. All neonates are being tested for antibodies using immunochemoluminiscency tests; if the mother is tested positive for SARS-CoV-2 RNA, a nasopharyngeal swab is also obtained from the child for RT-PCR analysis.Findings to date As of 22 October, 1167 women have been recruited (266, 354 and 547 for subcohorts 1, 2 and 3, respectively). Fourteen women tested positive to SARS-CoV-2 RNA by the day of delivery. All 14 children born from these women tested negative for SARS-CoV-2 RNA.Future plans Children from women included in subcohort 3 are expected to be recruited by the end of 2020. Children will be followed-up for 1 year in order to ascertain the effect that COVID-19 on their development.

Abstract Increasing urbanization worldwide calls for more sustainable urban development. Simultaneously, the global biodiversity crisis accentuates the need of fostering biodiversity within cities. Policies supporting urban nature conservation need to understand people's acceptance of biodiversity‐friendly greenspace management. We surveyed more than 2,000 people in 19 European cities about their attitudes toward near‐natural urban grassland management in public greenspaces, and related their responses to nine sociocultural parameters. Results reveal that people across Europe can support urban biodiversity, yet within the frames of a generally tidy appearance of public greenery. Younger people and those using greenspaces for a greater variety of activities were more likely to favor biodiversity‐friendly greenspace management. Additionally, people who were aware of the meaning of biodiversity and those stating responsibility for biodiversity conservation particularly supported biodiversity‐friendly greenspace management. Our results point at explicit measures like environmental education to increase public acceptance of policies that facilitate nature conservation within cities.

The globalization process, characterised by major worldwide interrelation and dependency, is entailing increasingly uniform economic, technological and cultural aspects. Territory nevertheless continues to be a different reality in each part of the planet due to natural factors (geomorphology, soil or climate), but also to human practices transforming this to adapt to local needs and circumstances. Each area thus generates diverse life experiences whose memory is reflected in the landscape, in urban areas or heritage, giving each place its specific character and identity. One of the determining factors in forming the landscape is water and it seems a universal fact that women are assigned many tasks involving water. In this curious interrelation between global and local spheres the study of washhouses is used for comprehensively characterising a particular landscape but with a specific use of space than concerns women’s work conditions and memory. The New Urban Agenda could provide a better sustainable urbanization linked with that.

This research starts out from an educational perspective: as literature a teachers in a Teacher Training College, we have noted the lack of diversity in family patterns in the text books. We have also observed how various stereotypes related to gender roles within families, jobs or the way in which gender itself expresses, are still present in the texts that schools offer to beginning readers. In this paper, we approach the Valencian literature for beginning readers in order to analyze the family structures and the treatment of roles of its members in various literary genres from books targeted at pre-school education (five years).

We consider a singular parabolic equation, for , arising in symmetric boundary layer flows. Here is a bounded domain with C2 boundary is bounded, and T > 0 is some fixed time. We establish sufficient conditions for the existence and uniqueness of a weak solution of this singular parabolic equation with Dirichlet boundary conditions, and we investigate its regularity. There are two different cases depending on β. If β < 1, for any initial data, there exists a unique weak solution, which in fact is a strong solution. The singularity is removable when β < 1. While if β = 1, there exists a unique solution of the singular parabolic problem The initial data cannot be arbitrarily chosen. In fact, if f is continuous and , as t → 0, then, this solution converges, as t → 0, to the solution of the elliptic problem, for , with Dirichlet boundary conditions. Hence, no initial data can be prescribed when β = 1, and the singularity in that case is strong.

We continue studying the existence of uniform L∞ a priori bounds for positive solutions of subcritical elliptic equations (P)p − \Delta_pu = f(u), in \Omega, u = 0, on ∂\Omega, We provide sufficient conditions for having a-priori L∞ bounds for C1,μ (\overline{\Omega }) positive solutions to a class of subcritical elliptic problems in bounded, convex, C2 domains. In this part II, we extend our results to Hamiltonian elliptic systems −\Delta u = f(v),−\Deltav = g(u), in \Omega, u = v = 0 on ∂\Omega, when f(v) = vp /[ln(e + v)]α, g(u) = uq/[ln(e + u)]β, with α, β > 2/(N − 2), and p, q are lying in the critical Sobolev hyperbolae 1/p+1 + 1/q+1 = N−2/N . For quasilinear elliptic equations involving the p-Laplacian, there exists a-priori bounds for positive solutions of (P)p when f(u) = up⋆−1/[ln(e + u)]α, with p∗ = Np/(N−p), and α > p/(N−p). We also study the asymptotic behavior of radially symmetric solutions uα = uα(r) of (P)2 as α → 0.

II Congreso de Alimentación, Nutrición y Dietética. Avances en Nutrición y Dietética Clínica: Prevención, Tratamiento y Gestión - Rol del Dietista-Nutricionista

This paper gives a survey over bifurcation problems for elliptic equations with nonlinear boundary conditions depending on a real parameter. We consider an elliptic equation with a nonlinear boundary condition which is asymptotically linear at infinity and which depends on a parameter. As the parameter crosses some critical values, there appear certain resonances in the equation producing solutions that bifurcate from infinity. We study the bifurcation branches, and characterize when they are sub- or supercritical. Furthermore, we apply these results and techniques to obtain Landesman-Lazer type conditions guarantying the existence of solutions in the resonant case and to obtain a uniform Anti-Maximum Principle and several results related to the spectral behavior when the potential at the boundary is perturbed. We also characterize the stability type of the solutions in the unbounded branches. In the remainder of this paper, we start our analysis on a sublinear oscillatory nonlinearity. We first focus our attention on the loss of Landesman-Lazer type conditions, and even in that situation, we are able to prove the existence of infinitely many resonant solutions and infinitely many turning points. Next we focus our attention on stability switches. Even in the absence of resonant solutions, we are able to provide sufficient conditions for the existence of sequences of stable solutions, unstable solutions, and turning points. We also discuss on bifurcation from the trivial solution set, and on a sublinear oscillatory nonlinearity. Finally, we states a formula for the derivative of a localized Steklov eigenvalue on a subset of the boundary, with respect to tangential variations of that subset. Resumen. Este artículo presenta un estudio sobre bifurcación para problemas elípticos con condiciones de frontera no-lineales. Consideramos una ecuación elíptica con condiciones de frontera no-lineales dependiendo de un parámetro. Supondremos que el término no lineal es asintóticamente lineal en el infinito. Cuando el parámetro cruza ciertos valores críticos (conocidos como los autovalores de Steklov) aparece un fenómeno de resonancia en la ecuación, lo que garantiza la existencia de ramas no acotadas de soluciones. Este fenómeno se conoce como bifurcación desde infinito. Estudiamos las ramas de soluciones y caracterizamos cuando son subcríticas (a la izquierda del autovalor) o supercríticas (a la derecha del autovalor). Aplicamos estos resultados para obtener condiciones del tipo Landesman-Lazer, que garantizan la existencia de soluciones para el problema resonante (cuando el parámetro coincide con el autovalor). Obtenemos también un Principio del Anti-Máximo, y resultados relativos al comportamiento espectral, cuando se perturba el potencial en la frontera. Además caracterizamos el tipo de estabilidad de las soluciones en dichas ramas no acotadas. En el resto del articulo, analizamos no linealidades oscilatorias y sublineales. Centramos nuestra atención en la pérdida de condiciones del tipo LandesmanLazer. Incluso en esta situación, demostramos la existencia de una sucesión de infinitas soluciones del problema resonante y una sucesión de infinitos puntos de retroceso. A continuación, analizamos los cambios de estabilidad. Incluso en ausencia de soluciones resonantes, proporcionamos condiciones suficientes para la existencia de una sucesión de infinitas soluciones estables, una sucesión de infinitas soluciones inestables y una sucesión de infinitos puntos de retroceso. También analizamos la bifurcación desde la solución trivial con una nolinealidad de tipo sublineal y oscilatorio. Finalmente establecemos una fórmula para la derivada del autovalor de Steklov localizado sobre un subconjunto de la frontera, con respecto a variaciones tangenciales del subconjunto.

We study a four-parameter bifurcation phenomenum arising in a system involving $p$-Laplacians: $$displaylines{ -Delta_p u = a phi_p(u)+ b phi_p(v) + f(a , phi_p (u), phi_p (v)) ,cr -Delta_p v = c phi_p(u) + d phi{p}(v)) + g(d , phi_p (u), phi_p (v)), }$$ with $u=v=0$ on the boundary of a bounded and sufficiently smooth domain in $mathbb{R}^N$; here $Delta_{p}u = { m div} (| abla u|^{p-2} abla u)$, with $p>1$ and $p eq 2$, is the $p$-Laplacian operator, and $phi_{p} (s) =|s|^{p-2} s$ with $p>1$. We assume that $a, b, c, d$ are real parameters, and use a bifurcation method to exhibit some nontrivial solutions. The associated eigenvalue problem, with $f=g equiv 0$, is also studied here.

Este artículo presenta un estudio sobre bifurcación para problemas elípticos con condiciones de frontera no-lineales. Consideramos una ecuación elíptica con condiciones de frontera no-lineales dependiendo de un parámetro. Supondremos que el término no lineal es asintóticamente lineal en el infinito. Cuando el parámetro cruza ciertos valores críticos (conocidos como los auto valores de Steklov) aparece un fenómeno de resonancia en la ecuación, lo que garantiza la existencia de ramas no acotadas de soluciones. Este fenómeno se conoce como bifurcación desde infinito. Estudiamos las ramas de soluciones y caracterizamos cuando son subcríticas (a la izquierda del autovalor) o supercríticas (a la derecha del autovalor). Aplicamos estos resultados para obtener condiciones del tipo Landesman-Lazer, que garantizan la existencia de soluciones para el problema resonante (cuando el parámetro coincide con el autovalor). Obtenemos también un Principio del Anti-Máximo, y resultados relativos al comportamiento espectral, cuando se perturba el potencial en la frontera. Además caracterizamos el tipo de estabilidad de las soluciones en dichas ramas no acotadas. En el resto del articulo, analizamos no linealidades oscilatorias y sublineales. Centramos nuestra atención en la pérdida de condiciones del tipo Landesman-Lazer. Incluso en esta situación, demostramos la existencia de una sucesión de infinitas soluciones del problema resonante y una sucesión de infinitos puntos de retroceso. A continuación, analizamos los cambios de estabilidad. Incluso en ausencia de soluciones resonantes, proporcionamos condiciones suficientes para la existencia de una sucesión de infinitas soluciones estables, una sucesión de infinitas soluciones inestables y una sucesión de infinitos puntos de retroceso. También analizamos la bifurcación desde la solución trivial con una no-linealidad de tipo sublineal y oscilatorio. Finalmente establecemos una fórmula para la derivada del autovalor de Steklov localizado sobre un subconjunto de la frontera, con respecto a variaciones tangenciales del subconjunto.