Multiplicity and concentration for Kirchhoff type equations around topologically critical points in potential
Multiplicity and concentration for Kirchhoff type equations around topologically critical points in potential
复制标题
基尔霍夫型方程围绕势势拓扑临界点的重数和浓度
DOI：
10.12775/tmna.2018.044
复制
发表时间：
2019
影响因子：
0.7
通讯作者：
Yanheng Ding
中科院分区：
文献类型：
--
作者：
Yu Chen;Yanheng Ding
本文研究了一类Kirchhoff型方程\[ -\varepsilon^2 M\n（\varepsilon^2-N}\int_{\mathbb{R}^N}\int_{\mathbb{R}^N}|\nabla v| ^2dx\n）\Delta v+V（x）v=f（v），\quad \mathrm{in }\ \mathbb{R}^N.在函数M，V和f的适当条件下，得到了正解集中在V的局部极大值点附近的存在性，从而肯定地回答了文fij中提出的问题.此外，我们还得到了势$V$的临界点集的拓扑对解的多重性的影响。
We consider the multiplicity and concentration of solutions for the Kirchhoff Type Equation \[ -\varepsilon^2 M\bigg( \varepsilon^{2-N}\int_{\mathbb{R}^N} |\nabla v|^2dx \bigg) \Delta v+V(x)v=f(v), \quad \mathrm{in }\ \mathbb{R}^N. \] Under suitable conditions on functions $M$, $V$ and $f$, we obtain the existence of positive solutions concentrating around the local maximum points of $V$, which gives an affirmative answer to the problem raised in \cite{fij}. Moreover, we also obtain multiplicity of solutions which are affected by the topology of critical points set of potential $V$.