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arXiv · 1209.3074

Standing Waves for nonlinear Schrodinger Equations involving critical growth

Jianjun Zhang·Zhijie Chen·Wenming Zou
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Abstract

We consider the following singularly perturbed nonlinear elliptic problem: $$-\e^2\Delta u+V(x)u=f(u),\ u\in H^1(\mathbb{R^N}),$$ where $N\ge 3$ and the nonlinearity $f$ is of critical growth. In this paper, we construct a solution $u_\e$ of the above problem which concentrates at an isolated component of positive local minimum points of $V$ as $\e\to 0$ under certain conditions on $f$. Our result completes the study made in some very recent works in the sense that, in those papers only the subcritical growth was considered

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Jianjun Zhang, Zhijie Chen, Wenming Zou. 2012-09-14. Standing Waves for nonlinear Schrodinger Equations involving critical growth. https://arxiv.org/abs/1209.3074

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