arXiv subjects

Zhouxin Li

Publications and source records attributed to Zhouxin Li.

2 recordsLinked to original sources

arXiv2017

Positive solutions for a class of singular quasilinear Schrödinger equations with critical Sobolev exponent

In this paper we prove the existence of positive solutions of the following singular quasilinear Schrödinger equations at critical growth \begin{eqnarray*} -Δu-λc(x)u-κα(Δ(|u|^{2α}))|u|^{2α-2}u = |u|^{q-2}u+|u|^{2^*-2}u,\quad u\in{D^{1,2}(\mathbb{R}}^N), \end{eqnarray*} via variational methods, where $λ\geq0$, $0<α<1/2$, $2<q<2^*$. It is interesting that we do not need to add a weight function to control $|u|^{q-2}u$.

math.AP↗

arXiv2013

Solutions for a class of quasilinear Schrödinger equations with critical exponents term

In this paper, we study a class of quasilinear Schrödinger equation of the form $$-\varepsilon^2Δu+V(x)u-\varepsilon^2(Δ(|u|^{2α}))|u|^{2α-2}u &=&λ|u|^{q-2}u+|u|^{2^*(2α)-2}u,\quad\mbox{in}{\mathbb{R}}^N, $$ where $\varepsilon>0,λ>0,q\geq2,α>1/2$ are constants, $N\geq3$. By using change of variable and variational approach, the existence of positive solution which has a local maximum point and decays exponentially is obtained.

math.AP↗