Unilateral global bifurcation and nodal solutions for the pp-Laplacian with sign-changing weight

In this paper, we shall establish a Dancer-type unilateral global bifurcation result for a class of quasilinear elliptic problems with sign-changing weight. Under some natural hypotheses on perturbation function, we show that $(\mu_k^\nu(p),0)$ is a bifurcation point of the above problems and there are two distinct unbounded continua, $(\mathcal{C}_{k}^\nu)^+$ and $(\mathcal{C}_{k}^\nu)^-$, consisting of the bifurcation branch $\mathcal{C}_{k}^\nu$ from $(\mu_k^\nu(p), 0)$, where $\mu_k^\nu(p)$ is the $k$-th positive or negative eigenvalue of the linear problem corresponding to the above problems, $\nu\in\{+,-\}$. As the applications of the above unilateral global bifurcation result, we study the existence of nodal solutions for a class of quasilinear elliptic problems with sign-changing weight. Moreover, based on the bifurcation result of Dr\'{a}bek and Huang (1997) [\ref{DH}], we study the existence of one-sign solutions for a class of high dimensional quasilinear elliptic problems with sign-changing weight

Research on Building Layout Driven by Energy Flow in Humid Tropics: Take the living space of HALE KUAHINE Dormitory in Honolulu as a thermal comfort simulating object

Building, which can be defined as a “container of life”, should not only be analyzed for expressing visual beauty of architectural language, but special attention related to living quality indoor and outdoor also must be asserted. The desire of comfort is usually satisfied by some mechanical equipment with high energy consumption in modern architecture; however, facing the current crisis of environmental pollution and energy shortage, it is urgent to blaze a trail and to find an architectural approach that is energy-efficient to enhance the life quality. As a part of the Shanghai-Hawaii Global Track Project, this doctoral research has been launched in University of Hawaii at Manoa (UHM), by selecting the non-air-conditioned dormitories in East-West Center (EWC) as an object to study the relation between the comfort level of daily activities and the building programming, which is one of the main architectural design contents once linked too much to spatial accessibility but lacking of considerations from a performance perspective. In order to find appropriate strategies for building programming in such a climate of humid tropics, the paper will blend the lessons of architectural history with the future-oriented technological progress, presenting in two major research clues ---- one is “experience” and the other is “evidence”. Specifically, the clue of “experience” will commence in studying the ancient ingenious ideas from typical human dwellings and vernacular settlements in hot-humid areas and then move to those salient modern regional explorations sparked by their ancestors’ wisdom. Meanwhile, the clue of “evidence” will serve as an evaluation system to demonstrate the feasibility of certain sustainable design concepts, with the assistance of computational simulation data and new credible discoveries from relevant disciplines such as environmental psychology, thermodynamics, neuroscience and behavioral economics on man-environment interaction. By mixing these expertise, architects can take the role of traditional engineers to fabricate a well-tempered “living machine” and figure out some constructive design techniques, which, if applied to mold the campus dormitory, would create a sense of well-being and encourage more students to enjoy the space for a longer time

Positive solutions of a nonlinear m-point boundary value problem

AbstractLet ai ≥ 0 for i = 1,…, m − 3 and am−2 > 0. Let ξi satisfy 0 < ξ1 < ξ2 < … < ξm−2 < 1 and Σm−2i=1 aiξi < 1. We study the existence of positive solutions to the boundary-value problem where a ϵ C([0, 1], [0, ∞)), and f ϵ C([0, ∞), [0, ∞)). We show the existence of at least one positive solution if f is either superlinear or sublinear by applying a fixed-point theorem in cones

Rich Feature Analysis as an Enabling Tool for Composition Teaching

Exploring the usage of language in light of its functions in specific pragmatic contexts, Systematic Functional Grammar (SFG) can be a promising tool for language teaching. Relying on this tool, teachers can promote learners’ linguistic awareness from the level of passive rule-following to that of explicit understanding, a level where they can see linguistic expression’s functional significance as explanation of their effectiveness. This paper is intended as a demonstration of such an explanatory procedure. Employing a SFG-based Rich Feature Analysis to examine students’ composition, it aims to show how we can efficiently and convincingly identify and explain some problematic constructions in their writing

Multiplicity of positive solutions for second-order three-point boundary value problems

AbstractWe study the multiplicity of positive solutions for the second-order three-point boundary value problem u″+λh(t)f(u)=0, t∈(0,1), u(0)=0, αu(η)=u(1)where η: 0 < η < 1, 0 < α < 1η. The methods employed are fixed-point index theorems and Leray-Schauder degree and upper and lower solutions