A class of fourth-order elliptic equations with concave and convex nonlinearities in $\mathbb{R}^N$
- 1 January 2021
- journal article
- research article
- Published by University of Szeged in Electronic Journal of Qualitative Theory of Differential Equations
- No. 71,p. 1-16
- https://doi.org/10.14232/ejqtde.2021.1.71
Abstract
In this article, we study the multiplicity of solutions for a class of fourth-order elliptic equations with concave and convex nonlinearities in $\mathbb{R}^N$. Under the appropriate assumption, we prove that there are at least two solutions for the equation by Nehari manifold and Ekeland variational principle, one of which is the ground state solution.
Keywords
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