Abstract
We investigate the following nonlinear biharmonic equations with pure power nonlinearities: \begin{equation*} \begin{cases} \triangle^2u-\triangle u+V(x)u= u^{p-1}u & \text{in } \mathbb{R}^N,\\ u>0 &\text{for } u\in H^2(\mathbb{R}^N), \end{cases} \end{equation*} where $2 < p< 2^*={2N}/({N-4})$. Under some suitable assumptions on $V(x)$, we obtain the existence of ground state solutions. The proof relies on the Pohožaev-Nehari manifold, the monotonic trick and the global compactness lemma, which is possibly different to other papers on this problem. Some recent results are extended.
Citation
Liping Xu. Haibo Chen. "Existence of positive ground solutions for biharmonic equations via Pohožaev-Nehari manifold." Topol. Methods Nonlinear Anal. 52 (2) 541 - 560, 2018. https://doi.org/10.12775/TMNA.2018.015