一类p-Kirchhoff方程基态解的存在性与唯一性

对于下面p-Kirchhoff型泛函■我们证明了约束在流形■上全局极小点或山路型临界点的存在性与唯一性,且这些临界点是某个Gagliardo-Nirenberg不等式的最优化子,特别当p∈(1,2]时,它们在不计平移意义下是唯一的.我们扩展了已有文献中p=2的情形的相关结果.

Existence and Uniqueness of Ground State Solutions for a Class of p-Kirchhoff Equations

For the following p-Kirchhoff type functional we prove the existence and uniqueness of global minimum or mountain pass type critical points on the L^p-normalized manifold S_c:={u∈W^1,p(Rⁿ):∫_Rⁿ|u|^pdx=c^p}. We show that these critical points indeed are optimizers of a certain Gagliardo-Nirenberg inequality. Especially, when p ∈ (1, 2], they are unique up to translations. We extend some known results for the case of p=2 in previous papers.