一类中立型方程的正解

本文研究具有正负系数的中立型微分方程，分别得到了这类方程存在和不存在正解的充分条件，并建立了不存在正解的比较定理。     

二阶非线性中立型时滞差分方程的正解

本文研究了一类二阶非线性中立型时滞差分方程的正解,得到了最终正解的存在性判据及存在正解的必要条件,建立了一些正解不存在性定理,所得结论推广并改进了已知的一些结果。     

一类中立型时滞差分方程的正解

研究一类中立型时滞差分方程面　　　　的正解,获得了方程存在最终正解以及非增正解的充要条件,建立了比较定理．     

一类泛函微分方程周期正解的存在性

本文研究了一类带参数的高维泛函微分程(1.1)的周期正解的存在性.利用一个著名的不动点指标定理,获得了该方程周期正解的存在性、多重性和不存在性.     

一类非线性无界时滞差分方程正解的不存在性

研究一类非线性无界时滞差分方程及其对偶方程，给出了方程不存在正解的充分条件，所得结论改进了有关的结果。     

全空间上一类非齐次椭圆方程正解的衰减

本文研究了非齐次椭圆方程不同衰减正解的存在性和衰减问题.利用上下解方法,得到了两个有着不同衰减的正解的存在性,推广了文献[2]中非齐次方程正解的存在性.     

一类非线性差分方程正解的不存在性

本文研究一类非线性差分方程及其对偶方程,给出了方程不存在正解的充分条件,所得结论改进了[1]的结果。     

不稳定型二阶中立型方程正解的存在性与有界振动

本文研究一类不稳定型二阶中立型微分方程正解的存在性与有界振动．证明了在一定条件下不稳定型二阶中立型方程总存在无界正解，并给出了保证其方程的一切有界解都振动的充分条件，改进了文［１，２］中的有关条件．     

一类二阶常微分方程无穷多点边值问题多个正解的存在性

研究了一类二阶非线性常微分方程无穷多点边值问题多个正解的存在性,运用不动点指数理论及Holder不等式得到了方程至少存在两个正解的若干充分条件,推广和改进了相关文献的结果.     

一类非线性椭圆方程正解的存在性

研究了一类非线性椭圆方程. 应用改进型Hardy不等式和变分方法, 证明了在一定条件下方程正解的存在性.     

非线性微分方程正解的不存在性

本文研究了非线性微分方程正解不存在性     

Nonexistence and existence of positive solutions for the Kirchhoff type equation

In this paper, we study the nonexistence and existence of positive solutions for the Kirchhoff type equation with nonlinearity having prescribed asymptotic behavior. Because of the structure of our equation, our nonexistence results have some special properties, and our conditions for positive solutions are also different from the existing results.     

Nonexistence of positive solutions to a quasilinear elliptic system and blow-up estimates for a non-Newtonian filtration system

The prior estimate and decay property of positive solutions are derived for a system of quasilinear elliptic differential equations first. Then the result of nonexistence for a differential equation system of radially nonincreasing positive solutions is implied. By using this nonexistence result, blow-up estimates for a class of quasilinear reaction-diffusion systems (non-Newtonian filtration systems) are established to extend the result of semilinear reaction-diffusion (Fujita type) systems.     

一类非牛顿渗流系统爆破界的估计

首先得到一类拟线性椭圆型方程组的正解的先验界估计和衰减性质,从而推出该方程组的径向非增正对称解的不存在性结果。利用此结果建立了一类拟线性反应扩散方程组（非牛顿渗流系统）的爆破界的估计,推广了半线性（Fujita型）反应扩散方程组的结果。     

Principal frequency and existence of solutions for quasilinear elliptic obstacle problems

In this paper, we are interested in the first eigenvalue of p-Laplacian and the relation between the first eigenvalue and the existence (or nonexistence) of nontrivial (positive) solution for quasilinear elliptic obstacle problems. Utilizing the fact that obstacle problem have consanguineous relations with corresponding equation, we get a simple approach to study the properties of solutions of obstacle problems, such as existence and nonexistence, regularity and stability, etc. In this paper we are mainly concerned with the existence and nonexistence.     

Positive solutions of the generalized Emden-Fowler equation in Hölder spaces

A singular sublinear BVP related to the Emden-Fowler equation is considered. Existence, nonexistence, and regularity of positive solutions in Hölder spaces is obtained.     

Global nonexistence for logarithmic wave equations with nonlinear damping and distributed delay terms

This paper is concerned with global nonexistence of solutions for a logarithmic wave equation with nonlinear damping and distributed delay terms. Due to the simultaneous presence of nonlinear damping and logarithmic source terms, we have difficulty in use of the concavity method. Applying the energy estimates, we show the global nonexistence of solutions with not only non-positive initial energy but also positive initial energy.     

Non-existence of positive radial solutions for a class of quasilinear elliptic system

In this paper, our main purpose is to establish some nonexistence results of positive radial solutions to the quasilinear ordinary differential equation system. The main results of the present paper are new and extend the previously known results.