Combined effects of concave and convex nonlinearities in nonperiodic fourth-order equations
Ruiting Jiang, Chengbo Zhaı · Electronic journal of qualitative theory of differential equations · 2018
In this paper, we consider the multiplicity of nontrivial solutions for a class of nonperiodic fourth-order equation with concave and convex nonlinearities. Based on the Nehari manifold and Ekeland variational principle, we prove that the equation has at least two solutions under some proper assumptions. Moreover, one solution is a ground state solution.