【摘要】 本文研究一类具有临界指数和不定位势的Kirchhoff型问题解的存在性。首先证明该问题的能量泛函满足山路结构；其次证明能量泛函满足局部(PS)_c条件，从而获得泛函的紧性条件；最后通过Ekeland变分原理和山路引理，得到该问题2个非平凡解的存在性。更多还原

【Abstract】 In this paper, the existence of solutions for a class of Kirchhoff type problems with critical exponent and indefinite potential is studied. Firstly, the energy functional is proved to satisfy the mountain pass geometry. Secondly, the compactness condition of function is obtained by proving that the energy functional satisfies the local(PS)_c condition. Finally, the existence of two nontrivial solutions is obtained via Ekeland’s variational principle and the mountain pass lemma.更多还原