具Keller-Osserman条件的拟线性椭圆系统的全局爆破解的存在性

假设f,g满足Keller-Osserman条件,我们证明半线性椭圆系统的全局爆破解的存在性:div(|x|-ap|▽u|p-2▽u)=m(x)f(u,v),div(|x|-ap|▽v|p-2▽v)=n(x)g(u,v),其中x∈RN,N≥2+p(a+1)/2,非线性f和g为正的连续函数,权函数m和n是连续函数。

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）.

完全非线性退化椭圆方程的粘性边界爆破解

研究了完全非线性退化椭圆方程的粘性边界爆破解问题.利用Keller-Osserman条件及比较原理证明了正粘性解的存在性与唯一性,并得到了边界爆破速率的估计.

一类k-Hessian方程解的存在性和渐近稳定性

该文考虑了边界爆破k-Hessian问题Sk(λ(D^(2)z))=b(x)f(z),x∈Ω,z|■Ω=+∞,其中,Ω■R^(N)是一个严格凸的光滑有界区域.文章通过单调迭代方法、上下解方法和Karamata正则变化理论得到了k-Hessian方程径向对称正解的存在性和严格凸的爆破正解的边界渐近行为.

Heisenberg群上分数阶Ginzburg-Landau方程解的有界性

本文证明Heisenberg群上分数阶的Keller-Osserman定理和Kato不等式,给出Heisenberg群上分数阶Ginzburg-Landau方程解的有界性.这个结果把欧氏空间上分数阶Ginzburg-Landau方程的结果推广到了Heisenberg群上.

具有奇性系数的半线性椭圆方程大解的存在性

研究了一类带奇性系数和一般梯度项的半线性椭圆方程大解的存在性.首先得到解的梯度估计,然后证明了方程在边界值等于n时解的存在性,最后利用上下解的方法得到了大解的存在性.