Positivity preserving properties have been conjectured for the bilaplace Dirichlet problem in many versions. In this note we show that in any dimension there exist bounded smooth domains Ω such that even the solution of ∆u = 1 in Ω with the homogeneous Dirichlet boundary conditions u = uν = 0 on ∂Ω is sign-changing. In two dimensions this corresponds to the Kirchhoff-Love model of a clamped pla...

We consider the elliptic problem $$ - \Delta_A u + = a_{\lambda}(x) |u|^{q-2}u+b_{\mu}(x) |u|^{p-2}u , for \(x \in \mathbb{R}^N\), \( 1 < q 2 p 2^*= 2N/(N-2)\), \(a_{\lambda}(x)\) is a sign-changing weight function, \(b_{\mu}(x)\) satisfies some additional conditions, \(u H^1_A(\mathbb{R}^N)\) and \(A:\mathbb{R}^N \to \mathbb{R}^N\) magnetic potential. Exploring Bahri-Li argument preliminary...

Multivariate sign functions are often used for robust estimation and inference. We propose using data dependent weights in association with such functions. The proposed weighted retain desirable robustness properties, while significantly improving efficiency inference compared to unweighted multivariate sign-based methods. Using signs, we demonstrate methods of location principal component anal...

We consider the semi-Riemannian Yamabe type equations of form −□u+λu=μ|u|p−1uonMwhere M is either semi-Euclidean space or pseudosphere dimension m≥3, □ Laplacian in M, λ≥0, μ∈R∖︀{0} and p>1. Using isoparametric functions on we reduce PDE into a generalized Emden–Fowler ODE w′′+q(r)w′+λw=μ|w|p−1wonI,where I⊂R [0,∞) [0,π], q(r) blows-up at 0 w subject to natural initial conditions w′(0)=0 first c...

Abstract This paper concerns semilinear elliptic equations involving sign-changing weight function and a nonlinearity of subcritical nature understood in generalized sense. Using an Orlicz–Sobolev space setting, we consider superlinear nonlinearities which do not have polynomial growth, state sufficient conditions guaranteeing the Palais–Smale condition. We study existence bifurcated branch cla...

how to cite this article: amini m, aliabadi f, alizade m, kalani m, qorbani m. the relationship between motor function and behavioral function in infants with low birth weight. iran j child neurol. autumn 2016; 10(4):49-55.   abstract objective nowadays, the evaluation of all aspects of infant development is important. however, in practice, some of these assessments, especially those requiring ...