Asymptotic profile of positive solutions of Lane-Emden problems in dimension two

We consider families $u_p$ of solutions to the problem \begin{equation}\label{problemAbstract} \left\{\begin{array}{lr}-\Delta u= u^p & \mbox{ in }\Omega\\ u>0 & \mbox{ in }\Omega\\ u=0 & \mbox{ on }\partial \Omega \end{array}\right.\tag{$\mathcal E_p$} \end{equation} where $p>1$ and $\Omega$ is a smooth bounded domain of $\mathbb R^2$. We give a complete description of the asymptotic behavior of $u_p$ as $p\rightarrow +\infty$, under the condition \[p\int_{\Omega} |\nabla u_p|^2\,dx\rightarrow \beta\in\mathbb R\qquad\mbox{ as $p\rightarrow +\infty$}.\

Exact Morse index computation for nodal radial solutions of Lane-Emden problems

We consider the semilinear Lane-Emden problem \begin{equation}\label{problemAbstract} \left\{\begin{array}{lr}-\Delta u= |u|^{p-1}u\qquad \mbox{ in }B u=0\qquad\qquad\qquad\mbox{ on }\partial B \end{array}\right.\tag{$\mathcal E_p$} \end{equation} where $B$ is the unit ball of $\mathbb R^N$, $N\geq2$, centered at the origin and $1<p<p_S$, with $p_S=+\infty$ if $N=2$ and $p_S=\frac{N+2}{N-2}$ if $N\geq3$. Our main result is to prove that in dimension $N=2$ the Morse index of the least energy sign-changing radial solution $u_p$ of \eqref{problemAbstract} is exactly $12$ if $p$ is sufficiently large. As an intermediate step we compute explicitly the first eigenvalue of a limit weighted problem in $\mathbb R^N$ in any dimension $N\geq2$

CoQ10 and Aging.

The aging process includes impairment in mitochondrial function, a reduction in anti-oxidant activity, and an increase in oxidative stress, marked by an increase in reactive oxygen species (ROS) production. Oxidative damage to macromolecules including DNA and electron transport proteins likely increases ROS production resulting in further damage. This oxidative theory of cell aging is supported by the fact that diseases associated with the aging process are marked by increased oxidative stress. Coenzyme Q10 (CoQ10) levels fall with aging in the human but this is not seen in all species or all tissues. It is unknown whether lower CoQ10 levels have a part to play in aging and disease or whether it is an inconsequential cellular response to aging. Despite the current lay public interest in supplementing with CoQ10, there is currently not enough evidence to recommend CoQ10 supplementation as an anti-aging anti-oxidant therapy

Asymptotic analysis and sign changing bubble towers for Lane-Emden problems

We consider the semilinear Lane-Emden problem in a smooth bounded domain of the plane. The aim of the paper is to analyze the asymptotic behavior of sign changing solutions as the exponent p of the nonlinearity goes to infinity. Among other results we show, under some symmetry assumptions on the domain, that the positive and negative parts of a family of symmetric solutions concentrate at the same point, as p goes to infinity, and the limit profile looks like a tower of two bubbles given by a superposition of a regular and a singular solution of the Liouville problem in the plane

Sign changing solutions of Lane Emden problems with interior nodal line and semilinear heat equations

We consider the semilinear Lane Emden problem in a smooth bounded simply connected domain in the plane, invariant by the action of a finite symmetry group G. We show that if the orbit of each point in the domain, under the action of the group G, has cardinality greater than or equal to four then, for p sufficiently large, there exists a sign changing solution of the problem with two nodal regions whose nodal line does not touch the boundary of the domain. This result is proved as a consequence of an analogous result for the associated parabolic problem

Contextos favorecedores da duplicação de objeto direto pleno de 3a pessoa no espanhol de Montevidéu

IX Congresso Brasileiro de Hispanistas realizado nos dias 22 a 25 agosto 2016O espanhol, segundo Fernández Soriano (1999) e Correa (2006), apresenta a possibilidade de duplicação do objeto, isto é, de uma correferência, em uma mesma oração, de um clítico e um sintagma em posição canônica de objeto. Para esses autores, quando o objeto é pronominal, a duplicação tem um caráter obrigatório, no entanto, quando o objeto é pleno, o objeto indireto duplicado é uma característica do espanhol de uma maneira geral, enquanto que a duplicação do objeto direto é recorrente apenas no espanhol falado na região rioplatense. Considerando o espanhol falado em Montevidéu como recorte, reunimos diferentes abordagens – JAEGGLI (1986), SUÑER (1988), FERNÁNDEZ SORIANO (1999), GROPPI (2001), CORREA (2006), ORDÓÑEZ (2012), entre outras – sobre as condições previstas para o contraste entre orações com e sem duplicação de objeto direto pleno. Para tais condições, há estudiosos que apontam o referente encabeçado pela preposição a, outros consideram o seu traço semântico de [+/ específico] e há, ainda, autores segundo os quais essas condições excedem a análise do referente do objeto. Tendo isto em vista, levantamos os contextos favorecedores da duplicação de objeto direto pleno de 3a pessoa no espanhol de Montevidéu para testar a hipótese de que essa duplicação ocorrerá em contextos de complemento [+específico], conforme propõe Suñer (1988, apud Groppi, 2001). Para alcançar tal objetivo, analisamos cinco entrevistas transcritas do Proyecto para el estudio sociolingüístico del español de España y América (PRESEEA). Dados iniciais da análise confirmam a hipótese até entãoUNILA­-UNIOEST