Ground states of bi-harmonic equations with critical exponential growth involving constant and trapping potentials

@article{Chen2019GroundSO,
title={Ground states of bi-harmonic equations with critical exponential growth involving constant and trapping potentials},
author={L. Chen and G. Lu and M. Zhu},
journal={arXiv: Analysis of PDEs},
year={2019}
}

In this paper, we first give a necessary and sufficient condition for the boundedness and the compactness for a class of nonlinear functionals in $H^{2}\ ( \mathbb{R}^{4}\right)$. Using this result and the principle of symmetric criticality, we can present a relationship between the existence of the nontrivial solutions to the semilinear bi-harmonic equation of the form \[ (-\Delta)^{2}u+\gamma u=f(u)\ \text{in}\ \mathbb{R}^{4} \] and the range of $\gamma\in \mathbb{R}^{+}$, where $f\ ( s\right… CONTINUE READING