Nonlinear Differential Equations and Applications NoDEA

, Volume 19, Issue 1, pp 19–47

Bound states to critical quasilinear Schrödinger equations


DOI: 10.1007/s00030-011-0116-3

Cite this article as:
Wang, Y. & Zou, W. Nonlinear Differ. Equ. Appl. (2012) 19: 19. doi:10.1007/s00030-011-0116-3


In this paper, we consider the critical quasilinear Schrödinger equations of the form
$$ -\varepsilon^2\Delta u+V(x)u-\varepsilon^2[\Delta(u^2)]u=|u|^{2(2^*)-2}u+g(u),\quad x\in \mathbb{R}^N, $$
where N ≥ 3, 2* := 2N/(N − 2) and g(u) is of subcritical growth. We prove the existence of positive bound states which concentrate around a local minimum point of V as ε → 0+.

Mathematics Subject Classification (2000)

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© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Department of Mathematical SciencesTsinghua UniversityBeijingChina