Local minimizers in spaces of symmetric functions and applications

We study $H^1$ versus $C^1$ local minimizers for functionals defined on spaces of symmetric functions, namely functions that are invariant by the action of some subgroups of $\mathcal{O}(N)$. These functionals, in many cases, are associated with some elliptic partial differential equations that may have supercritical growth. So we also prove some results on classical regularity for symmetric weak solutions for a general class of semilinear elliptic equations with possibly supercritical growth. We then apply these results to prove the existence of a large number of classical positive symmetric solutions to some concave-convex elliptic equations of H\'enon type

A supercritical Sobolev type inequality driven by the kk-Hessian equation

Our main purpose in this paper is to establish a supercritical Sobolev type inequality for the $k$-Hessian operator acting on $\Phi^{k}_{0,\mathrm{rad}}(B)$, the space of radially symmetric $k$-admissible functions on the unit ball $B\subset\mathbb{R}^{N}$. Besides, we prove both the existence of optimizers for the associated variational problem and the solvability of a related $k$-Hessian equation with supercritical growth

The Chacoan peccary, Catagonus wagneri (Mammalia, Tayassuidae), in the late Pleistocene (northern Uruguay, South America): paleoecological and paleobiogeographic considerations

Fil: Gasparini, Germán Mariano. División Paleontología Vertebrados. Facultad de Ciencias Naturales y Museo. Universidad Nacional de La Plata; ArgentinaFil: Ubilla, Martín. Facultad de Ciencias. Universidad de la República. Montevideo; UruguayFil: Tonni, Eduardo Pedro. División Paleontología Vertebrados. Facultad de Ciencias Naturales y Museo. Universidad Nacional de La Plata; Argentin

On a supercritical k-Hessian inequality of Trudinger-Moser type and extremal functions

We establish a supercritical Trudinger-Moser type inequality for the $k$-Hessian operator on the space of the $k$-admissible radially symmetric functions $\Phi^{k}_{0,\mathrm{rad}}(B)$, where $B$ is the unit ball in $\mathbb{R}^{N}$. We also prove the existence of extremal functions for this new supercritical inequality

O31 Integrative analysis reveals a molecular stratification of systemic autoimmune diseases

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Nonlinear Systems of Second-Order ODEs

<p/> <p>We study existence of positive solutions of the nonlinear system <inline-formula> <graphic file="1687-2770-2008-236386-i1.gif"/></inline-formula> in <inline-formula> <graphic file="1687-2770-2008-236386-i2.gif"/></inline-formula>; <inline-formula> <graphic file="1687-2770-2008-236386-i3.gif"/></inline-formula> in <inline-formula> <graphic file="1687-2770-2008-236386-i4.gif"/></inline-formula>; <inline-formula> <graphic file="1687-2770-2008-236386-i5.gif"/></inline-formula>, where <inline-formula> <graphic file="1687-2770-2008-236386-i6.gif"/></inline-formula> and <inline-formula> <graphic file="1687-2770-2008-236386-i7.gif"/></inline-formula>. Here, it is assumed that <inline-formula> <graphic file="1687-2770-2008-236386-i8.gif"/></inline-formula>, <inline-formula> <graphic file="1687-2770-2008-236386-i9.gif"/></inline-formula> are nonnegative continuous functions, <inline-formula> <graphic file="1687-2770-2008-236386-i10.gif"/></inline-formula>, <inline-formula> <graphic file="1687-2770-2008-236386-i11.gif"/></inline-formula> are positive continuous functions, <inline-formula> <graphic file="1687-2770-2008-236386-i12.gif"/></inline-formula>, <inline-formula> <graphic file="1687-2770-2008-236386-i13.gif"/></inline-formula>, and that the nonlinearities <inline-formula> <graphic file="1687-2770-2008-236386-i14.gif"/></inline-formula> satisfy superlinear hypotheses at <it>zero</it> and <inline-formula> <graphic file="1687-2770-2008-236386-i15.gif"/></inline-formula>. The existence of solutions will be obtained using a combination among the method of truncation, a priori bounded and Krasnosel'skii well-known result on fixed point indices in cones. The main contribution here is that we provide a treatment to the above system considering differential operators with nonlinear coefficients. Observe that these coefficients may not necessarily be bounded from below by a positive bound which is independent of <inline-formula> <graphic file="1687-2770-2008-236386-i16.gif"/></inline-formula> and <inline-formula> <graphic file="1687-2770-2008-236386-i17.gif"/></inline-formula>.</p

Alguns resultados de multiplicidade de soluções para equações eliticas quasilineares

Orientador : Djairo Guedes de FigueiredoTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação CientíficaDoutoradoDoutor em Ciência