带有薛定谔项的分数阶基尔霍夫方程解的存在性研究

A study of the existence of solutions for the fractional Kirchhoff equation with Schr?dinger term

针对带有薛定谔项和临界指数的分数阶基尔霍夫型问题进行了研究,把原方程转化为与该方程等价的方程组,当非线性项满足次临界、超线性和(AR)条件时,得到所对应的能量泛函具有山路几何结构,然后利用山路引理估计山路水平集,最后通过求解方程组得到原方程非平凡解的存在性和不存在性结果。

This paper studies the fractional Kirchhoff problem with Schr?dinger term and critical indexes.Firstly,the original equation is transformed into an equivalent equation set.When the nonlinear term satisfies subcritical,superlinear and(AR) conditions,a mountain pass geometry of the corresponding energy functional has,been obtained.Then,the mountain pass level set is estimated by the mountain pass lemma.Finally,the existence and nonexistence of nontrivial solutions of the original equation are obtained by solving the equation set.