Ordinary p-Laplacian systems with nonlinear boundary conditions

This paper is concerned with the existence of solutions for the boundary value problem

     

HOMOCLINIC ORBITS FOR A CLASS OF THE SECOND ORDER HAMILTONIAN SYSTEMS

The existence of homoclinic orbits is obtained by the variational approach for a class of second order Hamiltonian systems q(t)+▽V(t,q(t))=0,where V(t,x)=-K(t,x)+W(t,x),K(t,x) is neither a quadratic form in x nor periodic in t and W(t,x) is superquadratic in x.     

Multiple positive solutions for a semilinear elliptic equation with critical Sobolev exponent

In this paper, we study a class of semilinear elliptic equations with Hardy potential and critical Sobolev exponent. By means of the Ekeland variational principle and Mountain Pass theorem, multiple positive solutions are obtained.     

耦合非线性Schrödinger方程组的Neumann问题

该文考虑一类耦合椭圆型非线性Schr\"{o}dinger方程组的Neumann问题极小能量解（基态解）的存在性和集中性质. 主要研究极小能量解的尖点, 即最大值点的位置. 利用 Lin Tai-Chia 和 Wei Juncheng 研究 Dirichlet 问题的方法, 该文首先得到了相应Neumann问题的极小能量解的存在性. 当相当于Planck常数的小参数趋于零时, 该文证明了极小能量解的尖点向定义区域的边界靠近, 并且能量集中在这些尖点处. 另外, 方程组解的两个分支解相互吸引或排斥时, 它们的尖点也相互吸引或排斥.     

琅琊山景区不同叶绿素条件下树种叶片光谱差异分析

叶绿素含量高低反映植物健康状况,研究景区树种叶片叶绿素绝对值(SPAD)不同的光谱变化规律能为叶绿素高光谱监测波段识别与景区树种管理提供理论支撑。从琅琊山景区灌木和乔木类选取9个常见树种,探讨相同树种叶片SPAD值变化时的光谱差异,同时,横向对比相同SPAD值不同树种叶片的光谱特征,并深入分析不同树种叶片SPAD值与单波段原始光谱、光谱倒数、一阶微分、二阶微分及波段组合差值指数、归一化指数、比值指数、一阶微分归一化指数、一阶微分比值指数之间的关系。结果表明：9个所测树种叶片随着叶绿素SPAD值的升高,光谱变化规律各不相同,在可见光波段区分明显,总体上,光谱反射率最高的样本组SPAD值较低;叶绿素SPAD值相同时,在可见光波段,桂花较其余树种反射率整体较高; 在780~1 350 nm波段,广玉兰叶片反射率始终排前三,其余波段变化规律不明显;原始光谱反射率的二阶微分与海桐叶片SPAD值相关系数最大,一阶微分与其余8种相关性最高;与灌木、落叶乔木叶片SPAD值相关系数最大的光谱指数分别为差值指数、一阶微分归一化指数,与常绿乔木、不分树种相关系数最大的为一阶微分比值指数。     

Existence of positive solutions for a class of semilinear and quasilinear elliptic equations with supercritical case

In this paper, we consider a class of semilinear elliptic Dirichlet problems in a bounded regular domain with cylindrical symmetry involving concave-convex nonlinearities with supercritical growth. Using a new Sobolev embedding theorem and variational method, we show the existence of two positive solutions of the problem. Additionally, we study the quasilinear elliptic equation and obtain a similar result.