Strongly indefinite functionals and multiple solutions of elliptic systems

We study existence and multiplicity of solutions of the elliptic system (GRAPHICS) where Omega subset of R-N; Ngreater than or equal to3, is a smooth bounded domain and His an element ofC(1) ((Omega) over barx R-2, R). We assume that the nonlinear term (GRAPHICS) where p is an element of (1, 2*), 2* := 2N/(N-2), and q is an element of (1,infinity). So some supercritical systems are included. Nontrivial solutions are obtained. When H(x, u, v) is even in (u, v), we show that the system possesses a sequence of solutions associated with a sequence of positive energies (resp. negative energies) going toward infinity (resp. zero) if p>2 (resp. p<2). All results are proved using variational methods. Some new critical point theorems for strongly indefinite functionals are proved.35572973298

ELLIPTIC EQUATIONS AND SYSTEMS WITH CRITICAL TRUDINGER-MOSER NONLINEARITIES

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)In this article we give first a survey on recent results on some Trudinger-Moser type inequalities, and their importance in the study of nonlinear elliptic equations with nonlinearities which have critical growth in the sense of Trudinger-Moser. Furthermore, recent results concerning systems of such equations will be discussed.302SI455476INCTMatCoordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq

Weighted Sobolev spaces of radially symmetric functions

We prove dilation invariant inequalities involving radial functions, poliharmonic operators and weights that are powers of the distance from the origin. Then we discuss the existence of extremals and in some cases we compute the best constants.Comment: 38 page

Multiplicity of Positive Solutions for an Obstacle Problem in R

In this paper we establish the existence of two positive solutions for the obstacle problem \displaystyle \int_{\Re}\left[u'(v-u)'+(1+\lambda V(x))u(v-u)\right] \geq \displaystyle \int_{\Re} f(u)(v-u), \forall v\in \Ka where $f$ is a continuous function verifying some technical conditions and \Ka is the convex set given by \Ka =\left\{v\in H^{1}(\Re); v \geq \varphi \right\}, with $\varphi \in H^{1}(\Re)$ having nontrivial positive part with compact support in $\Re$. \vspace{0.2cm} \noindent \emph{2000 Mathematics Subject Classification} : 34B18, 35A15, 46E39. \noindent \emph{Key words}: Obstacle problem, Variational methods, Positive solutions.Comment: To appear in Progress in Nonlinear Differential Equations and their Application

Patients' perception regarding the influence of individual and social vulnerabilities on the adherence to tuberculosis treatment: a qualitative study

Background: Tuberculosis remains an important disease which mainly affects the majority of vulnerable individuals in society, who are subjected to poor living conditions and difficulties to access the services of public health. Under these circumstances, the present study aims to understand patients' perception in relation to the influence of individual and social vulnerabilities on the adherence to tuberculosis treatment. Methods: A qualitative descriptive cross sectional study was conducted in one large municipality at the state of Paraiba, Northeast of Brazil. The study subjects, who were residents of the study site, covered all tuberculosis cases diagnosed between March and June 2015. The sample was defined by the criteria of response saturation. All interviews were audio recorded, and data analysis was developed through the hermeneutic dialectic method and the theory of Generative Route Sense. The project was approved by the Research Ethics Committee of the University of Sao Paulo (USP). Results: A total of 13 individuals were interviewed and the responses were identified into two analytical categories: the difficulties they had and the enabling factors they could mention during their tuberculosis treatment. Patients brought up social exclusion as an obstacle to treatment adherence, which, along with stigmatization, weakened their link with family members and health professionals. Moreover, economic precariousness was a major hindrance to the maintenance of a proper diet and transportation access to health centers. However, social support and directly observed treatment helped to break down barriers of prejudice and to promote individual and family empowerment. Finally, patients also reported that their will to live and faith gave them the strength to continue with the treatment. Conclusions: According to patients in this study, social support and the strengthening of links with family members and health professionals may reduce social exclusion and other difficulties they face, thus encouraging them to the adhere to tuberculosis treatment.Univ Estadual Paraiba, Campina Grande, Paraiba, BrazilUniv Fed Rio Grande do Norte, Natal, RN, BrazilUniv Sao Paulo, Escola Enfermagem, Sao Paulo, SP, BrazilUniv Fed Sao Paulo, Escola Paulista Enfermagem, Sao Paulo, BrazilFac Santa Maria, Cajazeiras, Paraiba, BrazilUniv Fed Sao Paulo, Escola Paulista Enfermagem, Sao Paulo, BrazilWeb of Scienc