带双参数的非线性椭园型本征值问题

本文利用变分方法，将带双参数的非线性椭园本征值问题转化为约束极值问题，得出了非线性本征值问题的分歧解的存在性。     

SOLVABILITY FOR NONLINEAR ELLIPTIC EQUATION WITH BOUNDARY PERTURBATION

The solvability of nonlinear elliptic equation with boundary perturbation is consid- ered.The perturbed solution of original problem is obtained and the uniformly valid expansion of solution is proved.     

MULTIPLE LAYER BEHAVIOR OF BOUNDARY VALUE PROBLEM FOR SINGULARLY PERTURBED n-TH ORDER NONLINEAR DIFFERENTIAL EQUATION

In this paper,we study the singular perturbation of boundary value problem for a class of n-th order nonlinear differential equation,the solution is shown to exhibit multiple layer behavior.According to different layers and by introducing extended variable,we obtain the uniformly effective asymptotic expansion with different boundary layer correction term.     

Study of self—focusing in underwater waveguide by time reversal method

Acoustic wave time reversal self-focusing in underwater waveguide is studied.The acoustic wave time reversal is theoretically and experimentally investigated in a half-infinitefluid medium and a shallow fluid layer placed on a hard half-infinite solid medium,respectively,The ray approach method is adopted to study the far field of the acoustic field in theory,and the ultrasonic experiments have been carried out in laboratory to model the underwater waveguide.It is shown by theoretical and experimental results that the focusing gain can be improved by 12dB or more.     

Er3+,Yb3+共掺磷酸盐玻璃沟道波导放大器

在自行研制的Er3 ，Yb3 共掺磷酸盐玻璃基质上用离子交换方法制作出沟导光波导放大器。在110mW的抽运功率下(抽运光波长为980nm)，在1．8cm长的器件上获得了3．8dB的小信号(信号光波长为1．55μm)增益，单位长度上的增益为2．1dB／cm。     

Small Amplitude Solitons in the Higher-Order Nonlinear Schroedinger Equation in an Optical Fibre

By taking advantage of the approximate approach of small amplitude soliton, we study the higher-order nonlinear Schroeinger equation in an optical fibre. Our results show that the bright and dark solitons of small amplitude can appear on the background of a continuous wave in normal dispersion regime or in anomalous dispersion regime simultaneously due to the higher-order effects. Interesting connection between the higher-order nonlinear Schroedinger equation and the Korteweg-de Vries equation is also demonstrated.     

一个半正Sturm-Liouville边值问题的n个解的存在性

通过构造与非线性项有关的辅助函数并考察这个辅助函数在有界集上的性质，对于Sturm-Liouville边值问题建立了几个解的存在性，其中非线性项是下有界的．同时，给出了正解和非平凡解的一个判别方法．主要工具是锥压缩与锥拉伸型的Krasnosel’skii不动点定理．     

非线性非均衡蛛网模型的动态分析

描述单商品市场价格波动的蛛网模型是动态经济分析中的经典模型 ,证明了由模型 ( )所生成的价格序列在一定的条件下不会出现 3以上周期运动和混沌现象 ,并对其进行稳定性分析 ,得到模型关于均衡价格稳定的六个判别定理 .     

THE RELATION BETWEEN SIGN-CHANGING SOLUTION AND POSITIVE-NEGATIVE SOLUTIONS FOR NONLINEAR OPERATOR EQUATIONS AND ITS APPLICATIONS

By fixed point index theory and a result obtained by Amann, existence of the solution for a class of nonlinear operator equations x=Ax is discussed. Under suitable conditions, a couple of positive and negative solutions are obtained. Finally, the abstract result is applied to nonlinear Sturm-Liouville boundary value problem, and at least four distinct solutions are obtained.     

关于位势井及其对强阻尼非线性波动方程的应用

本文研究强阻尼非线性波动方程的初边值问题其中f(u)u≥0.首先用新的方法再次得到了位势井深度d的值,并首次得到了位势井内外结构.而后用位势井方法得到了问题的整体弱解,整体强解的存在性.最后证明了位势井W及井外集合V在问题(1)-(3)的流之下的不变性.