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Topological Methods in Nonlinear Analysis

Existence and Concentrate Behavior of Schrödinger equations with critical exponential growth in $\mathbb{R}^N$
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Existence and Concentrate Behavior of Schrödinger equations with critical exponential growth in $\mathbb{R}^N$

Authors

  • Jian Zhang
  • Wenming Zou

Keywords

Schrödinger equations, Critical growth, Ground state solution, Concentration

Abstract

We consider the nonlinear Schrödinger equation \begin{equation*} -\Delta u + (1+\mu g(x))u = f(u) \quad \text{in } \mathbb{R}^N, \end{equation*} where $N \ge 3$, $\mu \ge 0$; the function $g \ge 0$ has a potential well and $f$ has critical growth. By using variational methods, the existence and concentration behavior of the ground state solution are obtained.

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Published

2016-10-05

How to Cite

1.
ZHANG, Jian and ZOU, Wenming. Existence and Concentrate Behavior of Schrödinger equations with critical exponential growth in $\mathbb{R}^N$. Topological Methods in Nonlinear Analysis. Online. 5 October 2016. Vol. 48, no. 2, pp. 345 - 370. [Accessed 1 July 2025].
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