Multiple positive solutions for biharmonic equation of Kirchhoff type involving concave-convex nonlinearities

Abstract

In this article, we study the multiplicity of positive solutions for the biharmonic equation of Kirchhoff type involving concave-convex nonlinearities, ∆2u - (α + b ∫ℝN |∇u|2dx) ∆u + V(x)u = λƒ1(x)|u|q-2 u + ƒ2(x)|u|p-2u. Using the Nehari manifold, Ekeland variational principle, and the theory of Lagrange multipliers, we prove that there are at least two positive solutions, one of which is a positive ground state solution.