In this talk several existence theorems concerning the vortex solutions for some nonlinear PDE systems arising in the ABJM model will be presented.Firstly,w
In this talk,we study the degree counting formula of the rank two Toda system with simple singular sources.The key step is to derive the degree formula of t
We discuss work on existence and qualitative property of positive solutions for coupled nonlinear Schr(o)dinger equations.Depending upon the system being at
In critical point theory,Clarks theorem states as follows.Let X be a Banach space,Φ∈C1(X,R).Assume Φ satisfies the(PS)condition,is even and bounded from
In 1971,Serrin proved that certain overdetermined boundary value elliptic equations,considered on underlying regular bounded domains,must have radially symm
The search for time-harmonic solutions of nonlinear Maxwell equations in the absence of charges and currents leads to the following equation {▽×(μ(x)-1▽
I will first present a result on the existence of non-trivial global minimizers of Allen-Cahn equation in dimension 8.Then I will discuss related issues on
In this talk I will discuss some problems related to solutions with polynomial growth of the following elliptic system △u = uv2,△v = vu2,u,v>0 in Rn: Usin