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math.AP2013
A pointwise inequality for the fourth order Lane-Emden equation
Mostafa Fazly, Juncheng Wei, Xingwang Xu
We prove that the following pointwise inequality holds \begin{equation*} -Δu \ge \sqrt\frac{2}{(p+1)-c_n} |x|^{\frac{a}{2}} u^{\frac{p+1}{2}} + \frac{2}{n-4} \frac{|\nabla u|^2}{u}…
math.AP2011★ 2 cited
Classification of the stable solution to biharmonic problems in large dimensions
Juncheng Wei, Xingwang Xu, Wen Yang
We give a new bound on the exponent for the nonexistence of stable solutions to the biharmonic problem where .
math.AP2003★ 13 cited
The vortex dynamics of a Ginzburg-Landau system under pinning effect
Huaiyu Jian, Xingwang Xu
It is proved that the vortices are attracted by impurities or inhomogeities in the superconducting materials. The strong H^1-convergence for the corresponding Ginzburg-Landau syste…