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

Jian Zhang, Wenming Zou

DOI: http://dx.doi.org/10.12775/TMNA.2016.058

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.

Keywords


Schrödinger equations; Critical growth; Ground state solution; Concentration

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