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}
}
  • L. Chen, G. Lu, M. Zhu
  • Published 2019
  • Mathematics, Physics
  • arXiv: Analysis of PDEs
  • 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
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