A Kirchhoff-type problem involving concave-convex nonlinearities

Abstract

Abstract A Kirchhoff-type problem with concave-convex nonlinearities is studied. By constrained variational methods on a Nehari manifold, we prove that this problem has a sign-changing solution with least energy. Moreover, we show that the energy level of this sign-changing solution is strictly larger than the double energy level of the ground state solution.

Keywords

• Concave-convex nonlinearities
• Kirchhoff-type problem
• Nehari manifolds
• Ground state sign-changing solutions