球外部区域上一类椭圆边值问题的正径向解

研究了一类椭圆边值问题在球外部区域上正径向解的存在性,当非线性项f（u）关于u超线性或次线性增长的情形,获得了该问题正径向解的存在性.     

Existence and asymptotic properties of solutions for a nonlinear Schrödinger elliptic equation from geophysical fluid flows

In this paper, we study the existence and asymptotic behavior of radial solutions for a class of nonlinear Schrödinger elliptic equations on infinite domains describing the gyre of geophysical fluid flows. The existence theorem and asymptotic properties of radial positive solutions are established by using a new renormalization technique.     

A necessary and a sufficient condition for the existence of the positive radial solutions to Hessian equations and systems with weights

In this article, we consider the existence of positive radial solutions for Hessian equations and systems with weights and we give a necessary condition as well as a sufficient condition for a positive radial solution to be large. The method of proving theorems is essentially based on a successive approximation technique. Our results complete and improve a work published recently by Zhang and Zhou(existence of entire positive k-convex radial solutions to Hessian equations and systems with weights. Applied Mathematics Letters,Volume 50, December 2015, Pages 48–55).     

A Liouville theorem for a class of superlinear elliptic equations on cones

We give sufficient conditions for non-existence of positive solutions of the equation on a cone of We further analyze the existence of positive solutions in the radial, subcritical case, and show that under suitable conditions on the coefficients, every radial solution whose value in 0 is sufficiently large must vanish. Received April 2000     

A note on the radial solutions for the supercritical Hénon equation

We prove the existence of a positive radial solution for the Hénon equation with arbitrary growth. The solution is found by means of a shooting method and turns out to be an increasing function of the radial variable. Some numerical experiments suggest the existence of many positive oscillating solutions.     

某些半线性椭圆方程在环域上的正对径解的存在性

利用锥拉伸与锥压缩型的Krasnosel'skii不动点定理讨论了某些二阶非线性椭圆方程在环域上关于Dirichlet边界条件的正对径解的存在性。通过考察非线性项在有界闭区间上的性质建立了若干正对径解的存在性结论。主要结论不涉及非线性项的超线性增长和次线性增长。当非线性项存在极值并满足适当条件时,主要结论是非常有效的。     

非线性参数椭圆系统正解的存在性与多解性

本文讨论了一类非线性含参数椭圆系统正解的存在性与多解性,通过线性算子的谱半径,给出其正径向解存在与多解的条件,本质上改进和推广了文[1－3]的结果．     

Existence and Uniqueness of Positive Radial Solutions for a Class of Quasilinear Elliptic Systems

This article is concerned with the existence and uniqueness of positive radial solutions for a class of quasilinear elliptic system. With some reasonable assumptions on the nonlinear source functions and their coefficients, the existence and the upper and lower bounds of the positive solutions will be provided by using the fixed point theorem and the maximum principle for the quasilinear elliptic system.     

Radial solutions for a prescribed mean curvature equation with exponential nonlinearity

We establish an existence result for radial solutions for a prescribed mean curvature equation with exponential nonlinearity. Our methods are based on degree theory combined with a time map analysis. We also obtain two nonexistence results for positive solutions for more general f; one of them is not limited to radial solutions.     

Infinitely many positive solutions for a Schrödinger–Poisson system

We are interested in the existence of infinitely many positive non-radial solutions of a Schrödinger–Poisson system with a positive radial bounded external potential decaying at infinity.     

一类拟线性椭圆型方程组的正对称解的存在性

本文讨论了球域上一类拟线性椭圆型方程组正对称解的存在性和多解性     

Uniqueness of the ground state solutions of quasilinear Schrödinger equations

We are concerned with the uniqueness result of positive solutions for a class of quasilinear elliptic equation arising from plasma physics. We convert a quasilinear elliptic equation into a semilinear one and show the unique existence of positive radial solution for original equation under the suitable conditions on the power of nonlinearity and quasilinearity. We also investigate the non-degeneracy of a positive radial solution for a converted semilinear elliptic equation.     

Rn中△u+K(|x|)up=0的正奇解

本文利用不同的函数变换及Banach空间压缩影象原理,证明了Rm中半线性椭园方程△u+K(|x|)up=0无限多个奇解的存在性,并且具有渐进性广rn-2u(r)→c＞0(r→∞).     

Positive solutions of systems of singular Hammerstein integral equations with applications to semilinear elliptic equations in annuli

The existence of multiple positive solutions of systems of singular Hammerstein integral equations is studied, where the nonlinearities involved are allowed to have singularities in their second variables and satisfy weaker conditions involving the first eigenvalues of the corresponding linear Hammerstein integral operators. Such systems contain some mathematical models arising in science and engineering. Applications are given to the existence of multiple positive radial solutions of systems of semilinear singular elliptic equations in annuli on which, to the best of our knowledge, there has been little study.     

一类R~2上奇异非线性双调和方程正整解

以 Ｓｃｈａｕｄｅｒ－Ｔｙｃｈｏｎｏｆｆ不动点定理为工具,建立了一类Ｒ２上奇异非线性双调和方程正的径向对称整体解的存在定理,并给出了解的有关性质.     

一类奇异的半线性双调和方程的正整解

该文建立了一类奇异的半线性双调和方程正的径向对称整体解的存在性，并给出了解的有 关性质，推广了文献［７］的结果。     

The Dirichlet problem for supercritical biharmonic equations with power-type nonlinearity

For a semilinear biharmonic Dirichlet problem in the ball with supercritical power-type nonlinearity, we study existence/nonexistence, regularity and stability of radial positive minimal solutions. Moreover, qualitative properties, and in particular the precise asymptotic behaviour near x=0 for (possibly existing) singular radial solutions, are deduced. Dynamical systems arguments and a suitable Lyapunov (energy) function are employed.     

椭圆边值系统的正径向解的存在性与多解性

通过利用锥拉伸及锥压缩型的Krasnosel‘skii不动点定理，我们研究了一类椭圆边值系统的正径向解的存在性，非存在性与多解性。     

一类奇异非线性多重调和方程存在正整解的充分必要条件

研究一类奇异非线性多重调和方程?~mu=f(|x|,u,|▽u|)u~(-β),给出了方程存在正的径向对称整体解的充分必要条件和解的性质.