An Application of a Mountain Pass Theorem

We are concerned with the following Dirichlet problem: −Δu(x) = f(x, u), x∈Ω, u∈H ¹ ₀(Ω), (P) where f(x, t) ∈C (×ℝ), f(x, t)/t is nondecreasing in t∈ℝ and tends to an L ^∞-function q(x) uniformly in x∈Ω as t→ + ∞ (i.e., f(x, t) is asymptotically linear in t at infinity). In this case, an Ambrosetti-Rabinowitz-type condition, that is, for some θ > 2, M > 0, 0 > θF(x, s) ≤f(x, s)s, for all |s|≥M and x∈Ω, (AR) is no longer true, where F(x, s) = ∫ ^s ₀ f(x, t)dt. As is well known, (AR) is an important technical condition in applying Mountain Pass Theorem. In this paper, without assuming (AR) we prove, by using a variant version of Mountain Pass Theorem, that problem (P) has a positive solution under suitable conditions on f(x, t) and q(x). Our methods also work for the case where f(x, t) is superlinear in t at infinity, i.e., q(x) ≡ +∞. Received June 24, 1998, Accepted January 14, 2000.     

The role of buoyancy–frequency oscillations in the generation of mountain gravity waves

There is evidence from balloon measurements that atmospheric buoyancy–frequency profiles, apart from a sharp increase (roughly by a factor of two) at the tropopause, often feature appreciable oscillations (typical wavelength 1–2 km) with altitude. It is argued here that such short-scale oscillatory variations of the background buoyancy frequency, which usually are ignored in theoretical models, can have a profound effect on the generation of mountain waves owing to a resonance mechanism that comes into play at certain wind speeds depending on the dominant oscillation wavelength. A simple linear model assuming small sinusoidal buoyancy–frequency oscillations suggests, and numerical solutions of the Euler equations for more realistic flow conditions confirm, that under resonant conditions the induced gravity-wave activity is significantly increased above and upstream of the mountain, similarly to resonant flow of finite depth over topography.      

四川华蓥山地重力灾害类型及成因分析

从华蓥山所处的地理位置出发,全面的介绍了华蓥山地区近些年来的重力灾害发生的情况,可以看到重力灾害在本地区的影响之大,已经成为了本地区主要的灾害类型。通过各方面的调查研究,采用科学分析和经验指导相结合的方法,分析了引起重力灾害发生的各种因素,并重点从地质因素、水体因素、人为因素等3方面分析了华蓥山地重力灾害发生的成因,总结了可以引起重力灾害发生的外因和内因,可以看到重力灾害不单是某一个因素导致,而是由于众多的因素相互的影响所导致的。采取各种措施来预防灾害的发生,减少灾害给人类的生产和生活带来的危害。     

无界域上具有Sobolev临界指数的椭圆型方程解的存在性

本文利用山路引理和集中紧原理研究无界域上具有Sobolev临界指数的一类拟线性椭圆型方程的非平凡解的存在性。     

江西井冈山苔藓植物的初步调查

本文报导了作者在井冈山所采集的苔藓植物共172种,3变种及1亚种,并对其垂直分布作了初步的探讨。     

新疆和田昆仑山区苔藓植物的初步研究

报道了新疆和田南部山区昆仑山中段的苔藓植物共计４０种１变种１变型,它们隶属于１５属６科,其中的缺齿藓属Ｍｉｅｌｉｃｈｈｏｆｅｒｉａ为新疆新记录属,狭叶墙藓Ｔｏｒｔｕｌａ ｃｅｒｎｕａ等２０种为新疆新记录种。该地区苔藓植被的主要特点是;１．从区系组成来持,全部由藓类组成,其中以真藓科,丛藓科和柳叶藓科的植物占优势;尚未有苔类及色苔类植物的发现。２．从群落分布来看,主要是水边土生,干旱土生及水中岩面生     

地形对大别山区农村住房空间分布格局的影响

山区环境因素的限制使得农村住房呈现地域性的空间格局,确定农村住房空间分布格局及重要影响因素的关联性成为山区居民地规划管理的核心要素.以金寨县为例,结合高分辨率遥感影像目视解译、点格局分析以及相关分析等方法,通过引入地形要素(海拔、坡度、起伏度)因子,探索大别山区农村住房空间分布格局特征及地形要素的影响.系列实验结果表明:金寨县农村住房点间距离在0~140m时,住房呈现聚集分布的态势,表明大别山区农村住房之间因公共资源匮乏,受环境条件影响表现出较高的相互依赖性;而农村住房点间距离在140~400m时,住房呈现聚集、均匀、随机的多样性分布态势,表明大别山区农村住房缺乏宏观规划与分配;这种随机性趋势在400~10 000m的大尺度上表现得更为明显.相关分析表明,大别山区农村住房空间分布格局受制于局部地形条件,在海拔低、坡度小、起伏度低的地区,住房的聚集性较强,体现为相关分析的回归系数均达0.7左右;通过比较发现,地形要素对大别山区农村住房空间分布格局的影响强度由大到小为坡度起伏度海拔,坡度的决定系数达到0.6左右,对格局的影响强度是起伏度的1.1倍、海拔的1.13倍.本研究可为大别山区城镇规划提供科学依据.     

Existence Results for Quasilinear Elliptic Equations with Discontinuous Nonlinearities

The nonsmooth critical point theory is applied to prove the existence of solutions and multiple solutions of a quasilinear elliptic equation with discontinuous nonlinearities.     

Mountain pass solutions for a system of differential equations with Dirichlet boundary condition

In this article, the Dirichlet problem for a class of quasilinear differential equation systems is studied. Existence results are given by combining the dual least action principle and mountain pass theorem.     

Periodic and subharmonic solutions for a class of non-autonomous Hamiltonian systems

Some existence theorems are obtained for periodic and subharmonic solutions of a class of non-autonomous Hamiltonian systems. Our technical approach is based on a version of the Local Linking Theorem, and the Generalized Mountain Pass Theorem.