Multiplicity Results for Two Kinds of Kirchhnoff Type Equations

【作者】 李娜；

【导师】 张吉慧；

【作者基本信息】 南京师范大学 ， 应用数学， 2019， 硕士

【摘要】 我们考虑了带有临界指数的Kirchhoff型椭圆方程的多重性:其中a,b,λ>0,1<q<2,Ω(?)R4是一个包含原点的光滑有界区域.通过集中紧性原理和变分方法,我们得到了新的存在性结果.其次,我们又研究了下列四阶Kirchhoff型椭圆方程:其中a,b>0,位势V(x):R3→R从临界点理论的亏格性质出发,当V(x)和f(x,u)满足一定的条件时,得到了上述问题的多重解.更多还原

【Abstract】 We consider the multiplicity of the Kirchhoff type elliptic problem with critical growth:where a,b,λ>0,1<q<2,Ω(?)R4 is abounded domain with smooth boundary(?)Ω.By using the concentration compactness argument for PS sequences and variational methods,we obtain new existence results.Next,we also study the following fourth-order elliptic equations of Kirchhoff type:where a,b>0,we have the potential V(x):R3→R.Under certain assumptions on V(x)andf(x,u),we show the multiplicity of negative energy solutions for the above problem based on the genus properties in critical point theory.更多还原