On the indefinite Kirchhoff type equations with local sublinearity and linearity

Abstract

We consider a class of indefinite Kirchhoff-type equations:where , , and . We require that f(x, u) is “local" sublinear at the origin and “local" linear at infinity on u, respectively. Using mountain pass theorem and Ekeland variational principle, we obtain the existence and multiplicity of nontrivial solutions. In particular, the existence criterion of three nontrivial solutions is established. Furthermore, the nonexistence of nontrivial solutions is explored as well.