DSpace collection: 期刊論文

UNIQUENESS OF FINITE TOTAL CURVATURES AND THE STRUCTURE OF RADIAL SOLUTIONS FOR NONLINEAR ELLIPTIC EQUATIONS

title: UNIQUENESS OF FINITE TOTAL CURVATURES AND THE STRUCTURE OF RADIAL SOLUTIONS FOR NONLINEAR ELLIPTIC EQUATIONS abstract: In this article, we are concerned with the semilinear elliptic equation Delta u + K(|x|)|u|(p-1)u = 0 in R(n)\{0}, where n > 2, p > 1, and K(|x|) > 0 in R(n). The correspondence between the initial values of regularly positive radial solutions of the above equation and the associated finite total curvatures will be derived. In addition, we also conduct the zeros of radial solutions in terms of the initial data under specific conditions on K and p. Furthermore, based on the Pohozaev identity and openness for the regions of initial data corresponding to certain types of solutions, we obtain the whole structure of radial solutions depending on various situations.

Traveling waves for nonlinear cellular neural networks with distributed delays

title: Traveling waves for nonlinear cellular neural networks with distributed delays abstract: In this paper, we will establish the existence and nonexistence of traveling waves for nonlinear cellular neural networks with finite or infinite distributed delays. The dynamics of each given cell depends on itself and its nearest m left or I right neighborhood cells where delays exist in self-feedback and left or right neighborhood interactions. Our approach is to use Schauder's fixed point theorem coupled with upper and lower solutions of the integral equation in a suitable Banach space. Further, we obtain the exponential asymptotic behavior in the negative infinity and the existence of traveling waves for the minimal wave speed by the limiting argument. Our results improve and cover some previous works. (C) 2011 Published by Elsevier Inc.

TIME-DEPENDENT DOMAINS FOR NONLINEAR EVOLUTION OPERATORS AND PARTIAL DIFFERENTIAL EQUATIONS

title: TIME-DEPENDENT DOMAINS FOR NONLINEAR EVOLUTION OPERATORS AND PARTIAL DIFFERENTIAL EQUATIONS abstract: This article concerns the nonlinear evolution equation du(t)/dt is an element of A(t)u(t), 0 <= s < t < T, u(s) = u(0) in a real Banach space X, where the nonlinear, time-dependent, and multi-valued operator A(t) : D(A(t)) subset of X -> X has a time-dependent domain D(A(t)). It will be shown that, under certain assumptions on A(t), the equation has a strong solution. Illustrations are given of solving quasi-linear partial differential equations of parabolic type with time-dependent boundary conditions. Those partial differential equations are studied to a large extent.

THE EFM APPROACH FOR SINGLE-INDEX MODELS

title: THE EFM APPROACH FOR SINGLE-INDEX MODELS abstract: Single-index models are natural extensions of linear models and circumvent the so-called curse of dimensionality. They are becoming increasingly popular in many scientific fields including biostatistics, medicine, economics and financial econometrics. Estimating and testing the model index coefficients beta is one of the most important objectives in the statistical analysis. However, the commonly used assumption on the index coefficients, parallel to beta parallel to = 1, represents a nonregular problem: the true index is on the boundary of the unit ball. In this paper we introduce the EFM approach, a method of estimating functions, to study the single-index model. The procedure is to first relax the equality constraint to one with (d - 1) components of beta lying in an open unit ball, and then to construct the associated (d - 1) estimating functions by projecting the score function to the linear space spanned by the residuals with the unknown link being estimated by kernel estimating functions. The root-n consistency and asymptotic normality for the estimator obtained from solving the resulting estimating equations are achieved, and a Wilks type theorem for testing the index is demonstrated. A noticeable result we obtain is that our estimator for beta has smaller or equal limiting variance than the estimator of Carroll et al. [J. Amer Statist. Assoc. 92 (1997) 447-4891. A fixed-point iterative scheme for computing this estimator is proposed. This algorithm only involves one-dimensional nonparametric smoothers, thereby avoiding the data sparsity problem caused by high model dimensionality. Numerical studies based on simulation and on applications suggest that this new estimating system is quite powerful and easy to implement.