Application Of Critical Point Theory In Several Sublinear Equations

In this paper, we mainly consider two problems. Firstly, we concern the sublinear Schr¨odinger-Poisson equations:where λ is a parameter, V ∈ C(R~3, [0, +∞)), f ∈ C(R~3× R, R) and V-1(0) has nonempty interior. Under some suitable assumptions on f, we establish the existence of nontrivial solutions without the compactness of embedding of the working space. Furthermore, the concentration of solutions is explored on the set V-1(0) as λ â†' ∞ as well.Secondly, we consider the existence and multiplicity of periodic solutions of the nonautonomous second-order Hamiltonian systemsBy using the least action principle and minimax methods in critical point theory, some new existence and multiplicity theorems are obtained.