Boundary value problems with measures for elliptic equations with singular potentials

We study the boundary value problem with Radon measures for nonnegative solutions of $L_Vu:=-\Delta u+Vu=0$ in a bounded smooth domain \Gw, when $V$ is a locally bounded nonnegative function. Introducing some specific capacity, we give sufficient conditions on a Radon measure \gm on \prt\Gw so that the problem can be solved. We study the reduced measure associated to this equation as well as the boundary trace of positive solutions. In the appendix A. Ancona solves a question raised by M. Marcus and L. V\'eron concerning the vanishing set of the Poisson kernel of $L_V$ for an important class of potentials $V$.Comment: Contient un Appendice d'A. Ancona intitul\'e A necessary condition for the fine regularity of a boundary point with respect to a Schr\"odinger equatio

Large solutions of elliptic systems of second order and applications to the biharmonic equation

In this work we study the nonnegative solutions of the elliptic system \Delta u=|x|^{a}v^{\delta}, \Delta v=|x|^{b}u^{\mu} in the superlinear case \mu \delta>1, which blow up near the boundary of a domain of R^{N}, or at one isolated point. In the radial case we give the precise behavior of the large solutions near the boundary in any dimension N. We also show the existence of infinitely many solutions blowing up at 0. Furthermore, we show that there exists a global positive solution in R^{N}\{0}, large at 0, and we describe its behavior. We apply the results to the sign changing solutions of the biharmonic equation \Delta^2 u=|x|^{b}|u|^{\mu}. Our results are based on a new dynamical approach of the radial system by means of a quadratic system of order 4, combined with nonradial upper estimates

Backward blow-up estimates and initial trace for a parabolic system of reaction-diffusion

In this article we study the positive solutions of the parabolic semilinear system of competitive type \left\{\begin{array} [c]{c}% u_{t}-\Delta u+v^{p}=0, v_{t}-\Delta v+u^{q}=0, \end{array} \right. in $\Omega\times\left(0,T\right)$, where $\Omega$ is a domain of $\mathbb{R}^{N},$ and $p,q>0,$ $pq\neq1.$ Despite of the lack of comparison principles, we prove local upper estimates in the superlinear case $pq>1$ of the form $$u(x,t)\leqq Ct^{-(p+1)/(pq-1)},\qquad v(x,t)\leqq Ct^{-(q+1)/(pq-1)}$$ in $\omega\times\left(0,T_{1}\right) ,$ for any domain $\omega \subset\subset\Omega$ and $T_{1}\in\left(0,T\right) ,$ and $C=C(N,p,q,T_{1}$ For $p,q>1,$ we prove the existence of an initial trace at time 0, which is a Borel measure on $\Omega.$ Finally we prove that the punctual singularities at time $0$ are removable when $p,q\geqq1+2/N

Therapeutic drug monitoring in perianal fistulizing Crohn\u27s disease

Perianal fistulas are a common complication of Crohn\u27s disease (CD) that has, historically, been challenging to manage. Despite the strong available evidence that anti-tumor necrosis factor (anti-TNF) agents are useful in the treatment of perianal fistulizing Crohn\u27s disease (PFCD), a significant number of these patients do not respond to therapy. The use of therapeutic drug monitoring (TDM) in patients with CD receiving biologic agents has evolved and is currently positioned as an important tool to optimize and guide biologic treatment. Considering the treatment of PFCD can represent a challenge; identifying novel tools to improve the efficacy of current treatments is an important unmet need. Given its emerging role in other phenotypes of Crohn\u27s disease, the use of TDM could also offer an opportunity to enhance the effectiveness of available therapies and improve outcomes in the subset of patients with PFCD receiving biologics. Overall, there is mounting evidence that higher anti-TNF drug levels are associated with better rates of fistula healing . However, studies have been limited by their use of subjective outcomes and observational designs. Ultimately, further interventional, randomized controlled trials looking into the relationship between drug exposure and fistula outcomes are needed

Keller-Osserman estimates for some quasilinear elliptic systems

In this article we study quasilinear multipower systems of two equations of two types, in a domain $\Omega$ of R^{N} : with absorption terms, or mixed terms. Despite of the lack of comparison principle, we prove a priori estimates of Keller-Osserman type. Concerning the mixed system, we show that one of the solutions always satisfies Harnack inequality. In the case $\Omega$=B(0,1)\{0}, we also study the behaviour near 0 of the solutions of more general weighted systems, giving a priori estimates and removability results. Finally we prove the sharpness of the results

Control Interno y su relación con los inventarios en las Empresas Constructoras del Distrito de San Borja, año 2017

El presente trabajo de investigación, tiene por objetivo determinar de qué manera el control interno tiene relación con los inventarios en las empresas constructoras del distrito de san Borja, año 2017. La importancia del estudio radica en la necesidad de contar con un control interno eficiente en este sector, debido a las altas posibilidades de pérdidas de materiales, equipos y herramientas que ponen en riesgo los objetivos establecidos por la organización sino se realiza con periodicidad los controles necesarios para los inventarios y áreas encargadas que tienen las entidades. El tipo de investigación es correlacional descriptivo, el diseño de la investigación es no experimental transversal correlacional y el enfoque cuantitativo, con una población de 63 empresas constructoras del distrito de San Borja. Se empleó el muestreo probabilístico es decir que se eligió una muestra aleatoria estratificada compuesta por 54 empresas constructoras del distrito de san Borja en el año 2017. La técnica que se uso es la encuesta y el instrumento de recolección de datos, el cuestionario fue aplicado a las empresas. Para la validez de los instrumentos se utilizó el criterio de juicio de expertos. En la presente investigación se llegó a la conclusión que el control interno tiene relación con los inventarios en las empresas constructoras del distrito de San Borja, año 201

Some existence results of semilinear elliptic equations

We are concerned with the existence of positive solutions for equations of the form (1), defined in IRN and in IRN −{0}. We give a unified treatment of the problems studied before by others authors

On the uniqueness of sign changing bound state solutions of a semilinear equation

We establish the uniqueness of the higher radial bound state solutions of \Delta u +f(u)=0,\quad x\in \RR^n. \leqno(P) We assume that the nonlinearity $f\in C(-\infty,\infty)$ is an odd function satisfying some convexity and growth conditions, and either has one zero at $b>0$, is non positive and not identically 0 in $(0,b)$, and is differentiable and positive $[b,\infty)$, or is positive and differentiable in $[0,\infty)$

A new critical curve for a class of quasilinear elliptic systems

We study a class of systems of quasilinear differential inequalities associated to weakly coercive differential operators and power reaction terms. The main model cases are given by the $p$-Laplacian operator as well as the mean curvature operator in non parametric form. We prove that if the exponents lie under a certain curve, then the system has only the trivial solution. These results hold without any restriction provided the possible solutions are more regular. The underlying framework is the classical Euclidean case as well as the Carnot groups setting.Comment: 28 page