A priori estimates for some elliptic equations involving the pp-Laplacian

We consider the Dirichlet problem for positive solutions of the equation $-\Delta_p (u) = f(u)$ in a convex, bounded, smooth domain $\Omega \subset\R^N$, with $f$ locally Lipschitz continuous. \par We provide sufficient conditions guarantying $L^{\infty}$ a priori bounds for positive solutions of some elliptic equations involving the $p$-Laplacian and extend the class of known nonlinearities for which the solutions are $L^{\infty}$ a priori bounded. As a consequence we prove the existence of positive solutions in convex bounded domains

Resonant Solutions and Turning Points in an Elliptic Problem with Oscillatory Boundary Conditions

We consider the elliptic equation -Δu + u = 0 with nonlinear boundary conditions ∂u/∂n = λu + g(λ,x,u), where the nonlinear term g is oscillatory and satisfies g(λ,x,s)/s→0 as |s|→0. We provide sufficient conditions on g for the existence of sequences of resonant solutions and turning points accumulating to zero

Infinitely Many Stability Switches in a Problem with Sublinear Oscillatory Boundary Conditions

We consider the elliptic equation −u+u = 0 with nonlinear boundary condition ∂u ∂n = λu + g(λ, x, u), where g(λ,x,s) s → 0, as |s|→∞ and g is oscillatory. We provide sufficient conditions on g for the existence of unbounded sequences of stable solutions, unstable solutions, and turning points, even in the absence of resonant solutions

The importance of early parenting for later child outcomes: A study with Spanish families with children with disabilities

Children with different disability conditions have varied developmental trajectories, which perhaps influences parent-child interaction. For these and all infants, an optimal home environment that includes good parenting and positive parent-child interactions predicts better developmental outcomes (Spiker et al., 2005). Interventions using a family-centered, parenting-focused approach result in better parenting behavior that contributes to improved early child development (Avellar & Suplee, 2013; Roggman & Cardia, 2016). Information on parent-child interaction patterns is needed to guide intervention in natural contexts of families (Fuligni & Brooks-Gunn, 2013). Parent-child interaction data were collected from 44 mothers and 35 fathers interacting with their children (23 to 47 months) who had a disability and were in one of eight Spanish Early Interventions Centers. Mothers and fathers, separately, auto-recorded 10-minute play sessions at home. Parental interactions were assessed using PICCOLO (Roggman et al., 2013), a standardized measure of parenting. Two independent observers coded the interactions; strong intra-class correlation coefficients were found (.82 to .97 for mothers, .77 to .89 for fathers). The BSID-III scales (Bayley, 2015) assessed children’s development. Mothers scored slightly higher than did fathers. Scores varied by PICCOLO domains but were consistent with other PICCOLO studies of typical developing children (Roggman et al., 2013). Mother and father’s scores correlated indicating that the higher the scores of mothers in any dimension correlated with those of the parents combined. Positive significant Pearson correlations were found between parenting and child’s development with different patterns of father and mother domains predicting better language and cognitive outcomes. Although barriers to optimal parenting need further investigation, PICCOLO can be a useful tool to support optimal parenting.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Tiempo de la cultura

Cada verano la UC3M y el Círculo de Bellas Artes unen fuerzas para ofrecer cursos teóricos y talleres experimentales centrados en la creación. Este verano la oferta de cursos de la Escuela de las Artes está liderada por Rosa Torres Pardo y Eduardo Momeñe. Ambos artistas relatan el contenido de los cursos que imparten.Contiene: Tiempo de cultura. Propuestas (pp. 20-21) .-- Curso ‘Música en cine y cine en música’ / Rosa Torres Pardo (pp. 22-23) .-- Narrar el mundo / Eduardo Momeñe (pp. 24-27)

Acceso a la justicia de los más desfavorecidos y Union Europea

Uno de los derechos vinculados al de acceso a la justicia es el beneficio de gratuidad que permite que aquél se realice de forma efectiva también respecto de las personas que carecen de medios para litigar. Los distintos ordenamientos suelen garantizar el acceso a la justicia de los más desfavorecidos, ahora bien lo habitual es que limiten tal derecho a los litigios nacionales olvidando los cada vez más frecuentes litigios transnacionales 'piénsese en un proceso celbrado en Chile entre un chileno y un boliviano-. El presente artículo estudia la Directiva 2003/8/CE dictada en el ámbito de la Unión Europea relativa a la asistencia gratuita en litigios transfronterizos como posible ejemplo para futuras regulaciones que en el ámbito de latinoamérica puedan dictarse.One of the rights related to the access to Justice is to have it acceded it free of cost, which permits that the first also be achieved by those who have no means to litigate. The majority of the law orders use to ensure the access to Justice to the least-favoured people, although this right usually is limited to those conflicts where only national Court take part, excluding those where 'transnational' litigation ' more frequent nowadays ' take place (v. g., just imagine a process taking place in Chile, between a Chilean and a Bolivian). This paper approaches the Directive nº 2003/8/CE from European Union, about the pro bono legal assistance on transnational litigation as an example to future regulation to be approved on Latin America

Positive solutions of elliptic systems with superlinear terms on the critical hyperbola

We consider a slightly subcritical elliptic system with Dirichlet boundary conditions and a non-power nonlinearity in a bounded smooth domain. For this problem, standard compact embeddings cannot be used to guarantee the existence of solutions as in the case of power-type nonlinearities. Instead, we use the dual method on Orlicz spaces, showing that our problem possesses a mountain pass type solution

Dissipative solitons which cannot be trapped

In this paper we study the behavior of dissipative solitons in systems with high order nonlinear dissipation and show how they cannot survive under the effect of trapping potentials both of rigid wall type or asymptotically increasing ones. This provides an striking example of a soliton which cannot be trapped and only survives to the action of a weak potential