Anderson-like Transition for a Class of Random Sparse Models in d >= 2 Dimensions

We show that the Kronecker sum of d >= 2 copies of a random one-dimensional sparse model displays a spectral transition of the type predicted by Anderson, from absolutely continuous around the center of the band to pure point around the boundaries. Possible applications to physics and open problems are discussed briefly.

Existence and concentration of solutions for a class of biharmonic equations

Some superlinear fourth order elliptic equations are considered. A family of solutions is proved to exist and to concentrate at a point in the limit. The proof relies on variational methods and makes use of a weak version of the Ambrosetti-Rabinowitz condition. The existence and concentration of solutions are related to a suitable truncated equation. (C) 2012 Elsevier Inc. All rights reserved.

SUPERLINEAR ELLIPTIC PROBLEMS WITH SIGN CHANGING COEFFICIENTS

Via variational methods, we study multiplicity of solutions for the problem {-Delta u = lambda b(x)vertical bar u vertical bar(q-2)u + au + g(x, u) in Omega, u - 0 on partial derivative Omega, where a simple example for g( x, u) is |u|(p-2)u; here a, lambda are real parameters, 1 < q < 2 < p <= 2* and b(x) is a function in a suitable space L-sigma. We obtain a class of sign changing coefficients b(x) for which two non-negative solutions exist for any lambda > 0, and a total of five nontrivial solutions are obtained when lambda is small and a >= lambda(1). Note that this type of results are valid even in the critical case.

MULTIPLICITY OF NONRADIAL SOLUTIONS FOR A CLASS OF QUASILINEAR EQUATIONS ON ANNULUS WITH EXPONENTIAL CRITICAL GROWTH

In this paper, we establish the existence of many rotationally non-equivalent and nonradial solutions for the following class of quasilinear problems (p) {-Delta(N)u = lambda f(vertical bar x vertical bar, u) x is an element of Omega(r), u > 0 x is an element of Omega(r), u = 0 x is an element of Omega(r), where Omega(r) = {x is an element of R-N : r < vertical bar x vertical bar < r + 1}, N >= 2, N not equal 3, r >0, lambda > 0, Delta(N)u = div(vertical bar del u vertical bar(N-2)del u) is the N-Laplacian operator and f is a continuous function with exponential critical growth.

Perceived neighborhood problems: multilevel analysis to evaluate psychometric properties in a Southern adult Brazilian population

Abstract Background Physical attributes of the places in which people live, as well as their perceptions of them, may be important health determinants. The perception of place in which people dwell may impact on individual health and may be a more telling indicator for individual health than objective neighborhood characteristics. This paper aims to evaluate psychometric and ecometric properties of a scale on the perceptions of neighborhood problems in adults from Florianopolis, Southern Brazil. Methods Individual, census tract level (per capita monthly familiar income) and neighborhood problems perception (physical and social disorders) variables were investigated. Multilevel models (items nested within persons, persons nested within neighborhoods) were run to assess ecometric properties of variables assessing neighborhood problems. Results The response rate was 85.3%, (1,720 adults). Participants were distributed in 63 census tracts. Two scales were identified using 16 items: Physical Problems and Social Disorder. The ecometric properties of the scales satisfactory: 0.24 to 0.28 for the intra-class correlation and 0.94 to 0.96 for reliability. Higher values on the scales of problems in the physical and social domains were associated with younger age, more length of time residing in the same neighborhood and lower census tract income level. Conclusions The findings support the usefulness of these scales to measure physical and social disorder problems in neighborhoods.