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2018 Existence of positive ground solutions for biharmonic equations via Pohožaev-Nehari manifold
Liping Xu, Haibo Chen
Topol. Methods Nonlinear Anal. 52(2): 541-560 (2018). DOI: 10.12775/TMNA.2018.015

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.

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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

Information

Published: 2018
First available in Project Euclid: 6 November 2018

zbMATH: 07051679
MathSciNet: MR3915650
Digital Object Identifier: 10.12775/TMNA.2018.015

Rights: Copyright © 2018 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.52 • No. 2 • 2018
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