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.

Modeling the growth rate and lag time of different strains of Salmonella enterica and Listeria monocytogenes in ready-to-eat lettuce

The growth parameters (growth rate, mu and lag time, lambda) of three different strains each of Salmonella enterica and Listeria monocytogenes in minimally processed lettuce (MPL) and their changes as a function of temperature were modeled. MPL were packed under modified atmosphere (5% O-2, 15% CO2 and 80% N-2), stored at 7-30 degrees C and samples collected at different time intervals were enumerated for S. enterica and L monocytogenes. Growth curves and equations describing the relationship between mu and lambda as a function of temperature were constructed using the DMFit Excel add-in and through linear regression, respectively. The predicted growth parameters for the pathogens observed in this study were compared to ComBase, Pathogen modeling program (PMP) and data from the literature. High R-2 values (0.97 and 0.93) were observed for average growth curves of different strains of pathogens grown on MPL Secondary models of mu and lambda for both pathogens followed a linear trend with high R2 values (>0.90). Root mean square error (RMSE) showed that the models obtained are accurate and suitable for modeling the growth of S. enterica and L monocytogenes in MP lettuce. The current study provides growth models for these foodborne pathogens that can be used in microbial risk assessment. (C) 2011 Elsevier Ltd. All rights reserved.

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.

MULTI-BUMP SOLUTIONS FOR A CLASS OF QUASILINEAR EQUATIONS ON R

This paper is concerned with the existence of multi-bump solutions to a class of quasilinear Schrodinger equations in R. The proof relies on variational methods and combines some arguments given by del Pino and Felmer, Ding and Tanaka, and Sere.

Probabilistic crack growth analyses using a boundary element model: Applications in linear elastic fracture and fatigue problems

This paper addresses the numerical solution of random crack propagation problems using the coupling boundary element method (BEM) and reliability algorithms. Crack propagation phenomenon is efficiently modelled using BEM, due to its mesh reduction features. The BEM model is based on the dual BEM formulation, in which singular and hyper-singular integral equations are adopted to construct the system of algebraic equations. Two reliability algorithms are coupled with BEM model. The first is the well known response surface method, in which local, adaptive polynomial approximations of the mechanical response are constructed in search of the design point. Different experiment designs and adaptive schemes are considered. The alternative approach direct coupling, in which the limit state function remains implicit and its gradients are calculated directly from the numerical mechanical response, is also considered. The performance of both coupling methods is compared in application to some crack propagation problems. The investigation shows that direct coupling scheme converged for all problems studied, irrespective of the problem nonlinearity. The computational cost of direct coupling has shown to be a fraction of the cost of response surface solutions, regardless of experiment design or adaptive scheme considered. (C) 2012 Elsevier Ltd. All rights reserved.