一类Schr?dinger-Kirchhoff-Possion系统的非平凡解

Nontrivial Solutions for a Class of Schr?dinger-Kirchhoff-Possion Systems

运用变分法研究了一类Schr?dinger-Kirchhoff-Possion系统非平凡解的存在性.首先证明了该问题的能量泛函满足山路引理的几何结构.然后,通过一般的极小极大原理构造了一个具有Nehari流形和Poho?aev形相结合的渐近性质G(u_n)=o(1)的(PS)_c序列.最后证明该(PS)_c序列是有界的且有强收敛子列.

By means of variational methods, the existence of nontrivial solutions for a class ot SehrOdinger-Kirchhoff-Possion systems was considered. Firstly, it is proved that the energy functional corresponding to the problem possesses the geometric structure of the mountain pass lemma. Secondly, a （PS）c sequence satisfying asymptotic property G（un）： o（1） which combines Nehari manihold with Pohozaev manifold is obtained by the general minimax principle. Finally, it is proved that the （PS）c sequence is bounded and has strong convergent subsequence.