Multiple solutions for the p(x)−p(x)-laplace operator with critical growth

The aim of this paper is to extend previous results regarding the multiplicity of solutions for quasilinear elliptic problems with critical growth to the variable exponent case. We prove, in the spirit of \cite{DPFBS}, the existence of at least three nontrivial solutions to the following quasilinear elliptic equation $-\Delta_{p(x)} u = |u|^{q(x)-2}u +\lambda f(x,u)$ in a smooth bounded domain $\Omega$ of $\R^N$ with homogeneous Dirichlet boundary conditions on $\partial\Omega$. We assume that $\{q(x)=p^*(x)\}\not=\emptyset$, where $p^*(x)=Np(x)/(N-p(x))$ is the critical Sobolev exponent for variable exponents and $\Delta_{p(x)} u = {div}(|\nabla u|^{p(x)-2}\nabla u)$ is the $p(x)-$laplacian. The proof is based on variational arguments and the extension of concentration compactness method for variable exponent spaces

Existence of solution to a critical equation with variable exponent

In this paper we study the existence problem for the $p(x)-$Laplacian operator with a nonlinear critical source. We find a local condition on the exponents ensuring the existence of a nontrivial solution that shows that the Pohozaev obstruction does not holds in general in the variable exponent setting. The proof relies on the Concentration--Compactness Principle for variable exponents and the Mountain Pass Theorem

A mass transportation approach for Sobolev inequalities in variable exponent spaces

In this paper we provide a proof of the Sobolev-Poincar\'e inequality for variable exponent spaces by means of mass transportation methods. The importance of this approach is that the method is exible enough to deal with different inequalities. As an application, we also deduce the Sobolev-trace inequality improving the result obtained by Fan.Comment: 12 page

Epidemiología de Brucelosis y Leptospirosis humana y canina en Vela

La Brucelosis y la Leptospirosis son zoonosis de alto impacto en la salud animal y humana. La comunidad rural de Vela se encontraría potencialmente expuesta a estas enfermedades. Debido a esto se decidió realizar un análisis epidemiológico en la población humana y canina analizando la distribución espacial de la seropositividad para estas zoonosis, y los factores de riesgo asociados.Área: Ciencias Agrícolas, Produccion y Salud Anima

The concentration-compactness principle for Orlicz spaces and applications

In this paper we extend the well-known concentration -- compactness principle of P.L. Lions to Orlicz spaces. As an application we show an existence result to some critical elliptic problem with nonstandard growth.Comment: 20 pages. Submitted for publicatio

Nonstandard growth optimization problems with volume constraint

In this article we study some optimal design problems for nonstandard growth eigenvalues ruled by the $g-$Laplacian operator. More precisely, given $\Omega\subset \mathbb{R}^n$ and $\alpha,c>0$ we consider the optimization problem $\inf \{ \lambda_\Omega(\alpha,E)\colon E\subset \Omega, |E|=c \}$, where $\lambda_\Omega(\alpha,E)$ is the first eigenvalue to $$-\text{div}(g( |\nabla u |)\tfrac{\nabla u}{|\nabla u|}) + (1+\alpha \chi_E)g(u)\tfrac{u}{|u|} \quad \text{ in }\Omega$$ subject to Dirichlet, Neumann or Steklov boundary conditions. We analyze existence of solutions, symmetry properties of them, and the asymptotic behavior as $\alpha$ approaches $+\infty$.Comment: 17 page

Epidemiología de la leptospirosis humana de un área rururbana del partido de Tandil

El objetivo general es analizar la presentación de la leptospirosis en la comunidad rururbana de María Ignacia Vela. Específicamente se propuso estimar la prevalencia de anticuerpos anti-Leptospira spp. en los habitantes de la comunidad, conocer los serogrupos prevalentes y estudiar los factores de riesgo asociados