0000000000513165
AUTHOR
Changlin Xiang
showing 4 related works from this author
Quantitative Properties on the Steady States to A Schr\"odinger-Poisson-Slater System
2014
A relatively complete picture on the steady states of the following Schr$\ddot{o}$dinger-Poisson-Slater (SPS) system \[ \begin{cases} -\Delta Q+Q=VQ-C_{S}Q^{2}, & Q>0\text{ in }\mathbb{R}^{3}\\ Q(x)\to0, & \mbox{as }x\to\infty,\\ -\Delta V=Q^{2}, & \text{in }\mathbb{R}^{3}\\ V(x)\to0 & \mbox{as }x\to\infty. \end{cases} \] is given in this paper: existence, uniqueness, regularity and asymptotic behavior at infinity, where $C_{S}>0$ is a constant. To the author's knowledge, this is the first uniqueness result on SPS system.
Asymptotic behaviors of solutions to quasilinear elliptic equations with Hardy potential
2016
Optimal estimates on asymptotic behaviors of weak solutions both at the origin and at the infinity are obtained to the following quasilinear elliptic equations −Δpu − μ |x| p |u| p−2 u + m|u| p−2 u = f(u), x ∈ RN , where 1 0 and f is a continuous function. peerReviewed
Uniqueness of positive solutions to some Nonlinear Neumann Problems
2017
Using the moving plane method, we obtain a Liouville type theorem for nonnegative solutions of the Neumann problem ⎧ ⎨ ⎩ div (ya∇u(x, y)) = 0, x ∈ Rn,y > 0, lim y→0+yauy(x, y) = −f(u(x, 0)), x ∈ Rn, under general nonlinearity assumptions on the function f : R → R for any constant a ∈ (−1, 1). peerReviewed
Infinitely many solutions for p-Laplacian equation involving double critical terms and boundary geometry
2014
Let $1p^{2}+p,a(0)>0$ and $\Omega$ satisfies some geometry conditions if $0\in\partial\Omega$, say, all the principle curvatures of $\partial\Omega$ at $0$ are negative, then the above problem has infinitely many solutions.