A class of fourth-order elliptic equations with concave and convex nonlinearities in RN

摘要

In this article, we study the multiplicity of solutions for a class of fourth-order elliptic equations with concave and convex nonlinearities in RN. 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.