Semilinear parabolic problems in thin domains with a highly oscillatory boundary

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Patterns in parabolic problems with nonlinear boundary conditions

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Continuity properties on p for p-Laplacian parabolic problems

In this work we obtain some continuity properties on the parameter p at p = 2 for the Takeuchi-Yamada problem which is a degenerate p-Laplacian version of the Chafee-Infante problem. We prove the continuity of the flows and the equilibrium sets, and the upper semicontinuity of the global attractors. (C) 2009 Elsevier Ltd. All rights reserved.

On Global Attractors for a Class of Parabolic Problems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Saddle Point and Second Order Optimality in Nondifferentiable Nonlinear Abstract Multiobjective Optimization

This article deals with a vector optimization problem with cone constraints in a Banach space setting. By making use of a real-valued Lagrangian and the concept of generalized subconvex-like functions, weakly efficient solutions are characterized through saddle point type conditions. The results, jointly with the notion of generalized Hessian (introduced in [Cominetti, R., Correa, R.: A generalized second-order derivative in nonsmooth optimization. SIAM J. Control Optim. 28, 789–809 (1990)]), are applied to achieve second order necessary and sufficient optimality conditions (without requiring twice differentiability for the objective and constraining functions) for the particular case when the functionals involved are defined on a general Banach space into finite dimensional ones.

Lap number properties for p-Laplacian problems investigated by Lyapunov methods

In this work we consider a one-dimensional quasilinear parabolic equation and we prove that the lap number of any solution cannot increase through orbits as the time passes if the initial data is a continuous function. We deal with the lap number functional as a Lyapunov function, and apply lap number properties to reach an understanding on the asymptotic behavior of a particular problem. (c) 2006 Published by Elsevier Ltd.

Assessment of the effects of a parental intervention with mothers of children with internalizing problems

The present study assesses the effects of a semi-structured intervention held exclusively with mothers and its effects on internalizing problems, social skills of children, and positive and negative parenting practices. The single subject experimental design with three participants was adopted. The three mothers had, in baseline, children diagnosed with internalizing and externalizing problems. The instruments used were CBCL, RE-HSE-P, QRSH-Pais and PHQ-9, they were performed in baseline, pre-test, post-test, and follow-up assessments. The intervention held is characterized as semi-structured for it promotes the development of parental practices that are considered positive by the literature on behavior problems, however, contingently to the difficulties and demands of each case. The number of sessions performed for each case was 14, 15 and 17, which lasted about two hours each. The data were analyzed according to the instruments' norms and under the perspective of each singular case. The results found include remission of internalizing problems, increase in frequency of the children's social skills, increase in frequency of positive parental practices, and decrease in variability of negative parental practices. All the improvements were maintained on the six months follow-up, with the exception of variability on the negative parental practices of one client. Results are discussed in a context of mental health promotion and indicate the need for strategies to prevent internalizing problems in children.