期刊论文

Deng, Yinbin

英文

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS

1078-0947

2017

37

8

4213-4230

10.3934/dcds.2017179

Acknowledgments. The first author was supported by the Natural Science Foundation of China (11371160,11629101). The second author was partially supported by the excellent doctorial dissertation cultivation grant from Central China Normal University (2016YBZZ081).

本校为第一且通讯机构

In this paper, we study the following quasilinear elliptic equation with critical Sobolev exponent: $ -\Delta u +V(x)u-[\Delta(1+u^2)^{\frac 12}]\frac {u}{2(1+u^2)^\frac 12}=|u|^{2^*-2}u+|u|^{p-2}u, \quad x\in {{\mathbb{R}}^{N}}, $ which models the self-channeling of a high-power ultra short laser in matter, where N ≥ 3; 2 < p < 2* = $\frac{{2N}}{{N -2}}$ and V (x) is a given positive potential. Combining the change of variables and an abstract result developed by Jeanjean in [14], we obtain the existenc...