论文标题
具有Sobolev临界增长和合并非线性的非线性BiharmonicSchrödinger方程的归一化基态
Normalized ground states of nonlinear biharmonic Schrödinger equations with Sobolev critical growth and combined nonlinearities
论文作者
论文摘要
本文致力于研究以下非线性biharmonicschrödinger方程，并结合了功率类型的非线性\ begin {equation*} \ begin {Aligned} δ^{2} u-λu=μ| U |^{q-2} u+| U | u |^{4^* - 2} u \ quad \ quad \ mathrm {In} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {n} {n} $ 2 <q <2+ \ frac {8} {n} $，$ 4^*= \ frac {2n} {n-4} $是$ h^2 $ -Critical Sobolev Exponent，$λ$作为Lagrange Multiplier出现。通过分析基态能量相对于规定的质量的行为，我们确定了归一化基态溶液的存在。此外，所有基态都被证明是相关能量功能的局部最小值。
This paper is devoted to studying the following nonlinear biharmonic Schrödinger equation with combined power-type nonlinearities \begin{equation*} \begin{aligned} Δ^{2}u-λu=μ|u|^{q-2}u+|u|^{4^*-2}u\quad\mathrm{in}\ \mathbb{R}^{N}, \end{aligned} \end{equation*} where $N\geq5$, $μ>0$, $2<q<2+\frac{8}{N}$, $4^*=\frac{2N}{N-4}$ is the $H^2$-critical Sobolev exponent, and $λ$ appears as a Lagrange multiplier. By analyzing the behavior of the ground state energy with respect to the prescribed mass, we establish the existence of normalized ground state solutions. Furthermore, all ground states are proved to be local minima of the associated energy functional.
