Date: 27 May 2011

Bound states to critical quasilinear Schrödinger equations

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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+.

This article was supported by NSFC (No. 10871109, 11025106) and China Post-Doc Science Foundation (No. 20100470175).